in  I 


1111 ,. 

iiljjiii 

i!  fflliiiilM 


pjjpjil  l 

>.  mwm\\%MW 


! 

PIP  i  iiiiiHlB 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  CIVIL   ENGINEERING 

BERKELEY.  CALIFORNIA 


Engineering 
Library 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  CIVIL,  ENGINEERING 

BERKELEY.  CALIFORNIA 


WITHIN  THE  ATOM 

A  POPULAR  VIEW  OF  ELECTRONS  AND  QUANTA 


BY 


JOHN     MILLS 

M 

FELLOW,  AMERICAN  PHYSICAL  SOCIETY 

AUTHOR  "THE  REALITIES  OF  MODERN  SCIENCE' 


ILLUSTRATED 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

EIGHT  WARREN  STREET 

1921 


Mr 

Engineering 
Library 


COPYRIGHT,   1921,   BY 

0.  VAN  NOSTRAND  COMPANY 


PRINTED  IN  THE   UNITED  STATES  OF  AMERICA 


PREFACE 

THIS  volume  is  intended  for  readers  who  wish 
to  obtain  a  familiarity  with  the  basis  of  modern 
physical  science.  Without  mathematical  formula- 
tion it  deals  with  modern  theories  as  to  matter  and 
energy,  emphasizing  the  granular  structure  and 
electrical  nature  of  matter,  and  the  apparently 
corpuscular  character  of  energy. 

The  reader  need  have  no  previous  knowledge  of 
electricity,  mechanics,  or  chemistry.  For  the  appre- 
ciation of  the  evidence  of  certain  critical  experi- 
ments upon  which  modern  scientists  base  their  be- 
lief in  electrons  and  in  quanta  of  energy  some 
knowledge  of  electricity,  however,  is  required.  To 
supply  this  in  a  quick  and  easy  manner,  the  usual 
historical  order  of  presentation  is  abandoned  and 
the  correctness  of  modern  theories  is  assumed  at 
the  start.  There  are  postulated  the  electron  and  its 
counterpart,  the  proton.  In  terms  of  these  there 
are  then  described  those  few  phenomena  of  elec- 
tricity which  are  essential  to  the  later  consideration 
of  the  evidence.  In  this  way,  it  is  hoped  most 
rapidly  to  introduce  the  reader  to  modern  theories 
as  to  the  invisible  workings  of  the  physical  universe. 

J.  M. 

WYOMING,  N.  J. 
June,  1921. 


CONTENTS 


CHAPT1 

2R 

PREFACE         

PAGE 

iii 

INTRODUCTION    

vii 

I 

ATOMIC  STRUCTURES     

1 

II 

SATISFIED  AND  UNSATISFIED  SYSTEMS     .     . 

11 

III 

THE  PERIODIC  TABLE  OF  ATOMIC  SYSTEMS    . 

20 

IV 

MASS  AND  INERTIA  OF  ATOMIC  SYSTEMS   . 

37 

V 

RADIOACTIVE  DISINTEGRATIONS                 .  —^ 

48 

VI 

CONDUCTION  OF  ELECTRICITY  THROUGH  GASES 

57 

VII 

CONDUCTION  THROUGH  SOLIDS  AND  OTHER 

ELECTRICAL  PHENOMENA     

69 

VIII 

THE   PROOF   FOR   THE   EXISTENCE   OF    AN 

ELECTRON        

84 

IX 

ISOLATING  A  PROTON     

99 

X 

X-RAYS  AND  ATOMIC  NUMBERS    .... 

115 

BETWEEN  CHAPTERS  —  A  DIALOGUE    . 

135 

XI 

PHOTO-ELECTRIC  EFFECTS  AND  THE  QUAN- 

TUM OF  ENERGY       

139 

XII 

LIGHT  RADIATION  AND  ATOM  -MODELS    . 

155 

XIII 

MORE  EVIDENCE  FOR  THE  QUANTUM  HY- 

POTHESIS     

168 

XIV 

ENERGY  AND  ITS  AVAILABILITY    .... 

184 

APPENDIX  —  THE  MAGNITUDES  OF  ELECTRONS 

AND  QUANTA        

195 

GLOSSARY                                        .     .     . 

207 

INTRODUCTION 

IN  the  constellation  of  Orion  is  the  bright  reddish 
star  Betelgeuse.  For  centuries  it  served  with  other 
stars  as  a  guide  to  mariners  and  as  an  object  for 
consideration  by  philosophers  and  myth  makers. 
Although  we  still  retain  the  name  given  to  it  by 
the  Arabs  and  still  see  it  as  the  right  shoulder  of 
the  mighty  hunter,  science  has  removed  all  but  the 
nomenclature  of  the  earlier  animistic  interpretation 
and  substituted  cold  quantitative  facts.  Since  our 
school  days  we  have  known  that  Betelgeuse  is  a 
sun,  essentially  like  that  which  illuminates  our 
earth.  Very  recently  we  have  been  told  by  Pro- 
fessor Michelson  of  Chicago  as  to  its  astounding 
magnitude — three  hundred  times  the  diameter  of 
our  own  sun.  The  methods  by  which  he  arrived  at 
this  relationship  involve*  interesting  theories  and 
required  precise  experimentation.  Like  the  news- 
papers, however,  of  the  day  following  his  announce- 
ment let  us  be  content  for  the  moment  with  the 
fact  itself. 

In  the  midst  of  the  universe  in  which  Betelgeuse 
is  but  a  speck  exists  a  smaller  sun  on  a  planet  of 
which  there  crawl  what  Bertrand  Russell  aptly 
called  tiny  lumps  of  impure  carbons  and  water. 
What  a  shock  to  the  "ego-centricity"  of  these  car- 
bon compounds  to  realize  their  quantitative  in- 
significance in  comparison  with  Betelgeuse. 

vii 


viii  WITHIN  THE  ATOM 

About  this  larger  sun  there  are  probably  en- 
circling planets.  Are  there  organic  compounds  on 
any  of  these  and  how  do  they  arise  from  inorganic 
compounds  as  the  ageing  planet  slowly  cools?  Are 
there  conditions  of  temperature  and  atmospheric 
content  which  are  accompanied  by  such  chemical 
changes?  If  organic  substances  can  be  formed  will 
life  appear  on  the  planet?  What  intimations  of  the 
evolution  of  life  can  be  found  in  modern  science? 

Our  questions  grow  by  association,  overlapping 
one  another,  repeating  and  varying  their  content; 
and  our  apparently  unbound  speculation  leads  only 
to  further  questions.  Some  answers  and  much  ma- 
terial for  thought  are  vouched  by  modern  science 
although  the  specific  question  as  to  the  mechanism 
and  process  hi  the  evolution  of  life  remains  un- 
answered. 

What  in  fact  do  we  mean  by  life?  The  cater- 
pillar in  its  cocoon  awaits  the  proper  temperature 
for  its  metamorphosis:  the  radioactive  atom  spon- 
taneously emits  an  electron  and  becomes  a  new 
substance.  Both  caterpillar  and  radioactive  atom 
are  but  stages  in  a  sequence  of  events,  the  one  to 
be  followed  by  more  caterpillars  all  of  which  will 
differ  slightly  from  the  original  and  the  other  by 
more  atoms  which  will  differ  radically  from  the 
original.  The  comparison  is  not  too  seriously  in- 
tended although  it  is  safe  to  say  that  the  offspring 
of  the  radium  atom  will  be  moving  in  fast  circles 
ages  after  the  descendants  of  the  moth  have  per- 
ished from  the  face  of  the  earth. 

When  we  have  reached  a  satisfactory  definition 


INTRODUCTION  ix 

of  life  shall  death  be  its  negative?  Are  life  and 
death  merely  convenient  terms  which  we  loosely 
apply  to  phases  in  a  wide  process  of  continuous 
change?  and  what  are  the  entities  which  are  con- 
served during  the  change?  To  the  last  question 
science  today  may  apparently  give  answer  for  in 
energy  and  in  electricity  it  has  two  entities  which 
are  conserved  in  amount.  The  former  manifests 
itself  by  changes  in  the  location  of  the  latter,  for 
electricity  is  the  only  known  constituent  of  the 
ponderable  matter  of  which  our  universe  is  com- 
posed. 

Whether  we  are  interested  in  speculative  ques- 
tions like  those  just  mentioned,  in  less  speculative 
but  yet  unsolved  questions  like  the  mechanism  for 
the  transmission  of  stimuli  by  nerves,  or  in  the 
purely  practical  matter  of  the  efficient  organization 
and  operation  of  the  multiplicity  of  machines  which 
condition  our  daily  lives,  we  must  seek  explanations 
in  terms  of  energy  and  electricity. 

The  reduction  of  the  number  of  unknowns  with 
which  science  deals  is  a  recent  advance  which  has 
followed  discoveries  like  those  of  radium  and 
X-rays.  Widely  different  branches  of  science  are 
now  known  to  be  dealing  with  the  same  funda- 
mentals of  electricity  and  energy.  For  the  first  time 
in  centuries  there  exists  the  material  which  a  genius 
could  synthesize  into  a  universal  science,  in  which 
physics  and  chemistry,  biology  and  geology,  will 
lose  their  identities  in  a  common  set  of  principles. 

So  rapid,  however,  has  been  the  advance  of  sci- 
ence toward  this  simplification  of  terms  and  prin- 


x  WITHIN  THE  ATOM 

ciples  that  few  except  those  immediately  concerned 
are  aware  of  the  possibilities.  With  the  change  of 
base  and  point  of  view  which  has  followed  the  dis- 
covery of  the  electron,  and  the  consequent  interre- 
lation of  branches  of  science  long  held  apart,  there 
have  arisen  innumerable  questions  which  occupy 
the  time  of  those  best  able  to  expound  the  new 
science.  Our  schools  follow  but  tardily  in  their 
elementary  classes  the  conclusions  of  researchers  in 
science  and  our  text-book  writers  must  comply  with 
existing  distinctions  between  branches  of  science. 

The  fundamental  concepts  of  the  new  science  are 
easy  to  grasp  and  may  be  stated  in  relatively  simple 
terms,  although  the  quantitative  relationships  are 
to  be  expressed  only  in  mathematical  symbols.  The 
complete  synthesis  may  be  upon  us  some  day  as 
unexpectedly  as  were  Einstein's  hypotheses  and 
presumably  to  find  us  as  unprepared.  For  its 
critical  consideration  but  few  will  be  competent. 
For  a  more  popular  appraisal  many  of  us  may  be 
prepared  if  we  have  learned  to  think  of  all  scientific 
problems  in  terms  of  electricity  and  energy. 

Unfortunately  the  popularizer  of  these  concepts 
must  run  some  risk  of  false  statement  for  he  is 
limited  first  by  his  own  knowledge  and  interpreta- 
tion of  the  accepted  body  of  scientific  truth,  and 
second  by  the  necessity  of  purely  verbal  expression. 
Word  pictures  are  all  that  he  may  give  and  the 
selection  and  emphasis  of  their  material  may  carry 
implications  which  tune  shall  disprove. 

One  difficulty  which  confronts  those  who  would 
impart  the  concepts,  evidence,  and  conclusions  of 


INTRODUCTION  xi 

modern  science  to  readers  untrained  or  impatient  of 
mathematical  formulation,  arises  from  a  weakness 
which  is  characteristic  of  modern  research  itself. 
Science  today  is  quantitative  rather  than  qualita- 
tive. It  expresses  the  relationship  of  the  intensities 
of  two  phenomena,  as  for  example  the  intensities  of 
the  electric  current  and  of  the  illumination  of  an 
incandescent  lamp,  and  compensates  for  its  in- 
ability to  answer  the  question  "how"  by  its  wealth 
of  data  as  to  "how  much."  Research  monograph 
and  text-book  alike  emphasize  the  observable  quan- 
titative relationship  and  rarely  venture  far  into  the 
speculative  hinterland  where  "how"  must  precede 
"how  much."  As  we  teach  science  today  in  our 
schools  the  effort  of  learning  the  quantitative  rela- 
tionships too  frequently  leaves  neither  the  instruc- 
tor nor  the  student  leisure  for  fruitful  inquiry  or 
speculation  as  to  the  mechanism  itself. 

Rare  indeed  is  the  Faraday  whose  pictures  of  in- 
visible processes  satisfy  and  vivify  quantitative 
relationships  during  a  century  of  fruitful  research. 
That  particular  genius  was  discovered  by  Sir 
Humphrey  Davy,  himself  a  broad  and  versatile 
mind.  One  wonders  whether  our  phonographic 
classroom  methods  and  the  machine  processes  of 
our  laboratory  instruction  can  create  an  environ- 
ment for  that  inspiration  of  another  Faraday  which 
the  present  development  seems  to  require. 

Faraday's  pictures  were  in  the  nature  of  working 
hypotheses  as  to  an  all-embracing  and  continuous 
medium — an  elastic  ethereal  medium.  Assuming 
that  an  ether  existed,  the  attraction  or  repulsion  of 


xii  WITHIN  THE  ATOM 

electrified  bodies  was  explainable,  in  terms  of  the 
strains  which  the  bodies  introduced  into  the  me- 
dium, without  recourse  to  a  theory  for  action  at  a 
distance. 

During  the  later  half  of  the  19th  century,  the 
assumed  medium  became  of  first  importance  and 
scientifically  electricity  was  in  danger  of  becoming 
a  phenomenon  of  the  very  medium  which  had  been 
assumed  to  explain  its  own  phenomena.  The 
emphasis  on  the  medium,  however,  had  happy  re- 
sults for  it  led  Maxwell  to  the  conclusion  that  light 
was  an  electro-magnetic  phenomenon. 

With  the  discovery  of  the  electron — the  appar- 
ently indivisible  particle  of  electricity — the  ether 
rapidly  lost  its  importance  and  finally  with  the 
work  of  Einstein  it  has  ceased  to  be  a  necessary 
postulate  in  physical  science. 

The  terminology  of  the  older  physics  of  the  ether 
is  unavoidable,  however,  if  one  approaches  the  new 
physics  of  electrons  in  the  historical  order  of  its 
evolution.  Such  a  method  of  presentation  has  the 
advantage  that  the  experimental  evidence*  may  be 
set  forth  in  conjunction  with  each  statement  of  fact. 
On  the  other  hand,  the  method  demands  on  the 
part  of  the  reader  a  knowledge  of  the  phenomena 
and  laws  of  electricity,  mechanics,  and  chemistry 
which  is  seldom  possessed  by  the  hypothetical  per- 
son "the  general  reader."  This  deficiency  may,  of 
course,  be  supplied  by  devoting  to  that  purpose  the 
earlier  chapters  of  an  exposition,  but  several  of 
these  would  raise  memories  of  high  school  text- 
books. The  facts  which  must  be  acquired  would 


INTRODUCTION  xiii 

of  necessity  be  presented  in  a  conventional  manner. 
It  would,  therefore,  be  necessary  to  return  to  them, 
after  treating  the  fundamentals  of  the  new  science, 
and  attempt  a  corrective  interpretation  in  the  new 
terms.  The  process  would  not  only  be  wasteful  of 
time  but  difficult  of  attainment  for  first  impres- 
sions, even  of  science,  lie  deep  in  the  mind. 

It  is  perhaps  better  to  start  out  boldly,  stating 
the  physical  basis  of  the  new  science  and  building 
as  far  as  practical  on  its  firm  foundation.  For  cer- 
tain portions  of  the  superstructure  only  sketches 
are  available,  and  for  others  not  even  such  indica- 
tions. Occasionally  there  may  be  sketches  of  sev- 
eral draftsmen  neither  of  whom  seems  destined  to 
be  accepted  as  the  final  designer.  Enough  material, 
however,  may  be  inspected  by  the  reader  so  that 
he  may  appreciate  the  problem  of  the  new  science 
and  the  point  of  view.  Only  when  the  structure  is 
partially  completed  should  the  reader  be  expected 
to  recognize  its  relation  to  the  science  of  his  own 
school  days,  for  the  new  science  starts  with  the 
invisible  and  intangible  entity  of  electricity. 


WITHIN  THE  ATOM 

CHAPTER  I 

ATOMIC   STRUCTURES 

THE  story  is  told  of  the  debutante  who  met  the 
renowned  astronomer,  the  lion  of  the  evening,  with 
an  appreciative  remark  as  to  the  wonders  of  as- 
tronomy, "And  do  you  know  I  think  the  most 
wonderful  thing  is  how  we  know  the  names  of  the 
stars." 

Now  imagine,  if  you  can,  two  types  of  particles, 
each  invisible,  intangible  and  infinitesimal  in  the 
ordinary  senses  of  these  words,  and  indeterminate 
in  form  and  substance.  For  one  type,  wonderfully 
enough,  we  know  the  name  "electron,"  but  for 
the  other  type  there  is  no  agreement.  We  are 
free  to  choose  from  a  number  advanced  by  various 
scientists  and  shall  arbitrarily  adopt  the  term 
"proton." 

Electron  and  proton  are  complementary.  To- 
gether they  may  merge  in  a  union  so  close  that  their 
combined  size  is  less  than  that  of  the  electron  alone. 
Such  a  statement  may  sound  absurd  but  experi- 
ments seem  to  indicate  that  the  union  of  two  or 
more  protons  with  one  or  more  electrons  is  a  smaller 
particle  than  is  a  single  isolated  electron.  The  form 

1 


THE  ATOM 


and  size  of  the  electron  and  proton  must  then  be 
different  in  combination  from  that  of  the  free  elec- 
tron and  free  proton  respectively. 

We  apprehend  at  the  start  two  types  of  particles 
both  invisible  but  both  independently  observable 
by  certain  effects  which  they  produce.  To  these  we 
ascribe  complementary  properties.  In  so  doing  we 
meet  at  once  a  serious  difficulty  of  existing  language 
for  there  is  a  paucity  of  terms  by  which  we  may 
describe  the  particles  without  connotations  of  an 
animistic  bias.  The  protons  and  electrons  are  com- 
plementary, mutually  supplying  each  other's  needs. 
Electrons,  however,  are  mutually  antagonistic  and 
depart  from  each  other's  presence  unless  restrained. 
The  same  is  true  of  protons.  It  is  only  by  virtue  of 
the  complementary  properties  of  proton  and  elec- 
tron that  two  or  more  electrons,  for  example,  are 
constrained  to  the  same  infinitesimal  space. 

A  close  union  of  a  group  of  protons  and  electrons 
is  conceivable  from  a  social  parallel  for  it  may  re- 
semble geometrically  the  careful  seating  of  guests 
at  a  large  dinner.  Between  those  of  opposing  in- 
terests might  be  placed  others  whose  interests  are 
mutual  with  those  of  their  immediate  neighbors. 
The  dinner  guests  have  various  degrees  of  sym- 
pathy and  antipathy  for  each  other.  Between  elec- 
trons, however,  there  is  but  one  degree  of  antago- 
nism since  all  experiments  point  to  the  exact 
similarity  of  all  electrons  without  regard  to  then- 
individual  histories.  The  same  apparently  is  true 
of  protons  although  the  isolation  of  the  latter  has 
been  a  more  recent  advance  and  there  is  not  as 


ATOMIC  STRUCTURES  3 

large  a  volume  of  evidence  in  this  case.  We  are 
probably  entirely  safe  in  assuming  that  protons  are 
indistinguishable  and  are  interchangeable  to  an  ex- 
tent that  would  excite  the  admiration  of  the  piece- 
part  manufacturer  of  the  present  days  of  quantity 
production. 

Any  grouping  of  antagonistic  elements,  for  ex- 
ample, electrons,  can  persist  only  by  virtue  of  the 
presence  of  the  complementary  type,  in  this  case 
protons,  and  by  virtue  of  such  geometrical  arrange- 
ment that  the  opposing  tendencies  of  the  elements 
of  the  same  type  are  neutralized  by  the  complemen- 
tary tendencies  of  elements  of  a  different  type  and 
in  part  by  tendencies  which  are  discussed  on  page 
76.  According  to  some  theories,  however,  two  elec- 
trons or  two  protons  are  pictured  as  mutually  at- 
tracted when  they  are  very  close  together,  although 
at  larger  separations  they  are  repellent.  Similarly 
an  electron  and  a  proton  would  start  to  repel  each 
other  after  they  had  approached  to  within  a  certain 
small  distance  of  each  other.  In  any  case  the 
permanence  of  a  group  of  protons  and  electrons  will 
depend  upon  the  geometrical  arrangement.  The 
picture  which  we  may  form  is  like  that  of  some  state 
of  society  where  man  shuns  man,  and  woman  avoids 
woman,  but  unrestricted  promiscuity  prevails.  Pro- 
miscuity, however,  carries  no  stigma  for  individu- 
ality is  entirely  lacking. 

In  many  ways  their  society  approaches  an  angelic 
state,  for  its  members  are  not  confined  to  a  terres- 
trial plane  but  hover  and  flit  about  in  space,  subject 
to  the  opposing  tendencies  which  were  just  men* 


4  WITHIN  THE  ATOM 

tioned.  Nor  are  their  antagonisms  destructive  like 
those  of  humans,  despite  the  fact  that  electrons 
may  rush  about  with  a  speed  almost  that  of  light. 
Actual  collisions  between  like  elements  are  always 
avoided  by  swerving  to  one  side  or  in  the  extreme 
instances  of  head-on  approach  by  retracing  their 
paths.  A  deathless  existence  these  particles  lead 
and  although  there  is  marriage  and  giving  in  mar- 
riage the  unions  are  fruitless.  The  number  of  elec- 
trons or  of  protons  in  our  universe  is  believed  to  be 
eternally  fixed  so  that  their  immortal  society  may 
alter  only  in  its  configurations. 

Such  new  configurations  as  these  elements  may 
assume  are  formed  under  the  action  and  in  con- 
formity with  the  laws  stated  figuratively  above.  In 
more  classical  terms  these  may  be  expressed  by 
saying  that  like  elements  repel  and  unlike  attract. 
To  place  this  idea  completely  beyond  the  animistic 
bias  two  words  of  recent  coinage  and  incompletely 
sanctioned  usage  may  be  employed.  Electrons 
pellate,  protons  pellate,  but  an  electron  and  a 
proton  tractate. 

The  law  reminds  one  of  that  for  the  action  of 
electrical  charges,  since  like  charges  repel  and  un- 
like attract.  It  may  be  admitted  at  once  that  elec- 
trons are  elements  of  so-called  negative  electricity 
and  protons  elements  of  positive  electricity.  It  is 
preferable,  however,  to  consider  further  this  ques- 
tion of  configuration  of  these  elements  before  at- 
tempting to  relate  our  present  treatment  with  the 
familiar  facts  of  electricity.  We  shall  nevertheless 


ATOMIC  STRUCTURES  5 

find  it  most  convenient  to  speak  of  electrons  and 
protons  as  the  "electrical  elements." 

The  electrical  elements  are  found  associated  in 
configurations  which  increase  rapidly  in  complexity 
as  we  pass  from  the  simple  union  of  one  proton  and 
one  electron  to  systems  which  involve  hundreds  or 
thousands  of  elements.  When  more  than  one  pro- 
ton is  involved  two  types  of  systems  are  possible. 
In  the  simpler  type  all  the  protons  are  associated 
in  a  compact  group  which  comprizes  also  sufficient 
electrons  to  secure  a  certain  degree  of  stability  for 
the  coalition.  Such  other  electrons  as  may  be  asso- 
ciated with  the  system  under  consideration  are 
external  to  the  compact  group  or  nucleus  as  we  shall 
call  it.  This  simpler  type  of  system  we  shall  call 
atomic,  and  to  the  question  of  its  stability  we  shall 
return  later. 

The  second  type  of  system  is  that  which  involves 
two  or  more  nuclei  and  associated  external  elec- 
trons. Again  we  postpone  the  question  of  degree 
of  stability  and  class  such  systems  as  molecular. 

For  completeness  we  should  mention  at  this  point 
also  systems  which  may  be  formed  by  combinations 
of  the  two  main  types.  A  number  of  similar  sys- 
tems, for  example,  molecular  systems,  may  become 
closely  associated  by  a  temporary  relinquishment 
of  individual  freedom  and  form  a  federation,  to 
borrow  a  term  which  closely  fits.  As  long  as  the 
external  conditions  remain  as  they  were  this  federa- 
tion may  persist  but  its  component  members  may 
on  occasion  and  without  prejudice  assume  again 


6  WITHIN  THE  ATOM 

their  individual  existences.     Polymeric  systems  of 
this  kind  are  of  frequent  occurrence. 

As  the  opposite  of  polymerization  there  is  dis- 
sociation, the  process  of  separating  a  polymeric  or 
even  a  molecular  system  into  the  smaller  systems 
which  compose  it.  With  the  latter  process  particu- 
larly we  shall  have  more  to  do  later. 

For  the  moment,  however,  we  shall  consider  only 
the  simplest  type  of  system,  namely  the  atomic, 
which  is  formed  by  a  nucleus  and  a  number  of  elec- 
trons external  to  it.  In  the  nucleus  there  are  al- 
ways more  protons  than  electrons.  It  is  this  excess 
of  protons  that  serves  by  virtue  of  their  inherent 
complementary  characteristics  to  retain  in  the 
region  immediately  external  to  the  nucleus  a  num- 
ber of  electrons. 

Consideration  will  be  further  limited  by  exclud- 
ing for  the  present  all  systems  in  which  the  total 
number  of  electrons,  including  those  external  to 
the  nucleus  as  well  as  those  comprized  by  it,  is 
unequal  to  the  number  of  protons  in  the  nucleus. 
Systems  in  which  there  is  numerical  equality  be- 
tween protons  and  electrons  we  shall  call  normal 
atoms  or,  more  conventionally,  uncharged  atoms. 
We  shall  further  find  it  convenient  to  classify  such 
atomic  systems  by  the  number  of  electrons  external 
to  the  nucleus,  or  what  amounts  to  the  same  thing 
by  the  excess  of  protons  in  the  nucleus.  This  num- 
ber will  be  designated  the  "atomic  number." 

The  largest  known  atomic  number  is  92  and  this 
corresponds  to  the  chemical  element  uranium,  a 
metallic  element  found  in  pitchblende.  It  was  in 


ATOMIC  STRUCTURES  7 

residues  of  this  mineral,  from  which  the  uranium 
had  been  extracted,  that  Professor  and  Mme.  Curie 
discovered  the  element  radium.  Radium  has  an 
atomic  number  of  88.  Another  chemical  element, 
which  has  a  large  atomic  number,  is  thorium,  a  rare 
metal  used  in  making  incandescent  gas  mantles.  Its 
atomic  number  is  90. 

Atomic  systems  with  such  high  atomic  numbers 
are  very  rare  in  the  collector's  sense  of  the  word. 
Let  us  imagine  a  period  long  past  in  the  history  of 
our  universe  when  such  systems  predominated  even 
to  the  exclusion  of  systems  of  smaller  atomic  num- 
bers. Their  nuclei  were  crowded  spaces  filled  with 
antagonistic  electrical  elements — insecure  coalitions 
ready  if  necessary  to  sacrifice  some  of  their  mem- 
bers. Whether  under  external  influence  or  solely 
from  internal  causes  these  coalitions  started  to 
expel  their  members.  The  electrons  left  as  indi- 
viduals, ejected  with  enormous  velocity,  or  in  com- 
pany with  protons  with  smaller  velocities  as  be- 
fitted a  larger  party.  Such  a  party  was  apparently 
composed  of  four  protons  and  two  electrons,  and 
to  it  we  give  the  name  "alpha  particle." 

Under  some  conditions  the  reduced  coalition 
would  be  left  so  unstable  by  such  action  that  a 
further  expulsion  would  be  necessary  in  the  next 
few  seconds.  Sometimes  days  would  elapse  and 
under  other  conditions  years  or  even  ages  might 
pass  before  such  violent  readjustments  again  took 
place. 

Today  we  may  observe  the  same  process  in  the 
case  of  atomic  groups  of  high  atomic  numbers — 


8  WITHIN  THE  ATOM 

the  so-called  radioactive  elements.  The  changes 
in  nuclear  composition  appear  in  the  case  of  these 
elements  to  be  independent  of  external  conditions 
and  to  occur  solely  because  of  the  need  of  readjust- 
ment on  the  part  of  the  elements  of  the  nuclear 
coalition. 

By  a  sequence  of  expulsions  of  electrons  and  of 
alpha  particles  the  highly  complex  nuclei  of  the 
prehistoric  atomic  systems  were  reduced  in  number 
of  electrical  elements  and  increased  in  stability  until 
finally  the  apparently  stable  atomic  structures  of 
our  ordinary  chemical  elements  were  attained.  In 
other  words,  we  may  consider  the  chemical  elements 
like  tin,  lead,  sulphur  and  oxygen  to  be  "end- 
products"  of  a  long  series  of  radioactive  changes. 
The  character  of  these  changes  and  the  alterations 
in  the  properties  of  the  atomic  systems  which  result 
will  be  discussed  in  considerable  detail  in  later 
chapters. 

Although  the  disruption  of  the  complex  nuclear 
structure  of  a  radioactive  atom  is  spontaneous  in 
the  sense  of  occurring  without  the  stimulus  of  ex- 
ternal agents,  similar  disturbances  do  not  occur 
simultaneously  in  all  the  individual  atoms  of  a  large 
group.  Some  of  the  atoms  of  a  bit  of  uranium, 
for  example,  or  of  radium,  are  always  breaking 
down.  The  product  of  the  disintegration  may  be 
removed  by  trained  experimenters  and  hence  the 
rate  at  which  it  is  formed  may  be  measured.  Know- 
ing the  rate  at  which  disintegration  is  occurring,  it 
is  a  matter  of  simple  mathematics  to  calculate  the 
average  life,  that  is  the  time  required  until  half 


ATOMIC  STRUCTURES  9 

the  original  atomic  systems  will  have  disintegrated. 
This  is  using  the  term  "average  life"  as  actuaries 
do,  for  of  course  some  of  the  atoms  may  last  for 
ages  without  dissociating. 

In  the  case  of  radium  the  average  life  is  estimated 
as  about  1600  years;  that  is,  it  should  require  that 
time  for  half  the  atoms  of  any  bit  of  radium  to 
become  changed  into  atomic  systems  of  smaller 
numbers  of  elements.  Curiously  enough  the  next 
atomic  system,  a  gaseous  element  known  as  "niton," 
has  a  short  average  life  of  only  five  or  six  days.  The 
atomic  number  of  niton  is  86,  for  it  is  the  result  of 
the  ejection  of  an  alpha  particle  from  the  nucleus 
of  the  radium  system,  which  has  an  excess  of  88 
protons. 

The  alpha  particle  is  itself  an  atomic  system,  al- 
though it  is  not  a  normal  or  uncharged  atom  since 
it  involves  more  protons  than  electrons.  If  two 
external  electrons  are  associated  with  it,  it  becomes 
a  normal  atom,  namely  that  of  helium,  a  light  in- 
active gaseous  element  which  has  recently  attracted 
public  attention  as  a  desirable  substitute  in  filling 
balloons  for  the  lighter  but  active  element  hydrogen 
which  burns  with  oxygen. 

It  was  perhaps  by  such  spontaneous  changes  in 
the  composition  of  the  nuclei  of  atomic  systems, 
as  are  illustrated  today  by  radium,  that  the  known 
chemical  elements  were  produced.  The  definition, 
however,  of  the  term  "chemical  element"  is  no 
longer  as  simple  as  it  was  in  the  days  before  this 
disintegration  theory  was  advanced  and  accepted 
by  scientists.  Until  we  have  discussed  with  further 


10  WITHIN  THE  ATOM 

detail  the  possible  changes  which  may  occur  in 
atomic  systems,  we  may  use  the  term  in  its  usual 
sense,  and  say  that  the  eighty,  or  so,  known  chem- 
ical elements  are  the  products  of  radioactive  dis- 
integration for  which  the  further  disintegration  is 
so  slow  as  to  be  negligible  or  inappreciable.  For 
all  practical  purposes,  however,  we  may  assume 
that  our  chemical  elements  are  end-products  of  pre- 
historic disintegration. 


CHAPTER  II 

SATISFIED  AND  UNSATISFIED  SYSTEMS 

IT  is  difficult  to  describe  the  interactions  of  the 
electrical  elements  without  recourse  to  words  which 
have  an  emotional  significance.  Words  like  stable 
and  unstable,  or  active  and  inert,  might  be  used 
but  they  have  scientific  connotations  which  are  bet- 
ter avoided  at  present.  In  continuing  the  discussion 
of  atomic  systems  we  shall  use  words  which  are 
frankly  animistic  and  classify  these  systems  as  sat- 
isfied, unsatisfied,  or  dissatisfied.  The  radioactive 
systems  which  were  described  in  the  previous  chap- 
ter are  evidently  violently  dissatisfied  systems. 

A  failure  of  satisfaction  may  be  the  result  of  a 
deficiency  in  the  quantity  or  in  the  quality  of  the 
desired  good.  Quantitatively  an  electrical  system 
is  satisfied  if  there  is  an  equality  in  the  number  of 
protons  and  electrons  which  comprise  it.  Satisfac- 
tion as  to  quality,  on  the  other  hand,  depends  upon 
the  configuration  of  the  component  elements  of  the 
system. 

Dissatisfaction  when  it  occurs  is  deep  seated — 
a  neurotic  condition  of  the  nucleus  which  may  re- 
sult without  any  external  stimulus  in  violent  out- 
bursts and  a  veritable  orgy  of  smashing  china  and 
throwing  things  about.  This  excitable  state  is 

11 


12  WITHIN  THE  ATOM 

characteristic  of  those  atomic  systems  which  have 
retained  their  youth  and  been  unchanged  by  the 
years.  When  they  shall  have  become  as  lead,  a 
long  peaceful  life  will  confront  them,  in  which  they 
may  be  at  times  unsatisfied  but  practically  never 
dissatisfied.  During  the  formative  years  of  their 
discontent  the  nature  of  their  dissatisfaction  adapts 
itself  to  their  condition,  being  now  concerned  with 
quantity  and  again  with  quality  or  configuration. 
At  times  they  throw  off  alpha  particles  and  thus 
find  themselves  with  an  excess  of  electrons  which 
are  a  source  of  dissatisfaction  in  their  innermost 
and  nuclear  hearts.  The  electron  which  is  then  ex- 
pelled from  the  nucleus  is  sometimes  spoken  of  as 
a  beta  particle.  By  expulsions  of  alpha  and  beta 
particles  the  radioactive  systems  lose  much  of  their 
energy  and  all  appearances  of  radicalism. 

For  a  time,  however,  we  shall  deal  with  the  con- 
servative atoms  which  never  become  more  than 
mildly  unsatisfied.  Systems  which  are  unsatisfied 
in  the  numerical  equivalence  of  protons  and  elec- 
trons show  the  effect  of  electrical  charges.  The 
consideration  of  these  effects  also  must  be  post- 
poned and  our  attention  fixed  upon  systems  which 
are  satisfied  in  this  quantitative  relationship  but 
are  unsatisfied  in  the  configuration  of  their  com- 
ponent elements.  Such  absence  of  satisfaction  as 
then  exists  is  solely  a  matter  of  the  arrangement  of 
the  electrons  external  to  the  nucleus  since,  if  the 
source  of  the  trouble  were  in  the  latter,  dissatisfac- 
tion would  be  manifest  unmistakably. 

The  electrons  which  are  external  to  the  nucleus 


SATISFIED  AND  UNSATISFIED  SYSTEMS      13 

of  an  atom  are  separated  from  it  and  from  each 
other  by  relatively  large  distances.  Perhaps  as  good 
a  picture  of  an  atomic  system  as  may  be  easily 
formed  is  obtained  by  a  comparison  with  our  solar 
system.  The  distances  between  sun  and  planets 
and  between  the  various  planets  are  very  large  as 
compared  to  the  diameters  of  any  of  the  planetary 
bodies.  If  we  now  imagine  the  sun  to  be  very  small 
as  compared  to  the  earth  and  then  imagine  all  the 
distances  and  sizes  to  be  proportionally  reduced 
until  the  system  is  invisible  even  with  the  most 
powerful  microscope  we  have  a  possible  picture  of 
an  atomic  system.  The  sun  is  first  made  smaller 
because  the  nucleus  is  small  compared  to  the  elec- 
tron. Some  dimensions  of  such  a  system  are  quite 
accurately  known  for  they  are  determinable  by 
methods  which  will  be  described  later. 

The  diameter  of  the  atom  depends  upon  its  con- 
struction, being  smaller  for  some  chemical  elements 
than  for  others.  If  we  wished,  for  example,  to  keep 
out  of  the  way  of  a  hammer  thrower,  starting  his 
turns,  we  would  assume  that  his  diameter  was  that 
of  the  circle  through  which  the  hammer  head 
swung.  In  much  the  same  way  the  diameter  of 
any  atom  is  that  of  the  circle  of  which  the  center  is 
the  nucleus  and  the  radius  the  distance  to  the  outer- 
most electron. 

The  hydrogen  atom  is  composed  of  only  one 
proton  and  one  electron.  The  two  elements  are 
probably  whirling  about  each  other  in  space  much 
like  a  rapidly  whirling  dumbbell  except  that  there 
is  no  direct  connection  between  the  ends  of  the 


14  WITHIN  THE  ATOM 

dumbbell.  Its  diameter  is  about  two  hundredths  of 
a  millionth  of  a  centimeter,  but  this  is  about  one 
hundred  thousand  times  as  large  as  that  of  the 
electron  so  that  the  diameter  of  an  electron  is  about 
two  tenths  of  a  millionth  of  a  millionth  of  a  centi- 
meter. 

The  other  atoms  are  not  so  simple.  The  helium 
atom,  of  which  we  have  spoken  before,  consists  of 
a  nucleus  and  two  external  electrons.  The  atom  of 
sodium  has  eleven,  and  that  of  chlorine  seventeen 
electrons,  external  to  the  nucleus.  We  do  not  know 
as  much  about  the  arrangement  of  the  electrons  in 
the  atomic  structures  as  we  should  like  or  as  we 
probably  shall  in  the  near  future.  For  the  purpose 
of  discussing  the  effects  of  the  configuration  of  the 
external  electrons  we  may,  however,  draw  one  or 
two  parallels  of  a  kindergarten  nature  which  will 
serve  in  default  of  more  authoritative  pictures. 

The  system  of  nucleus  and  external  electrons  may 
be  likened  to  a  few  children  playing  a  circle  game 
about  a  teacher.  Suppose  that  the  game  goes  best 
with  eight  in  the  ring  but  is  possible  with  any  num- 
ber between  six  and  ten.  If  ten  are  playing,  that 
is  if  the  teacher's  responsibility  is  for  ten,  as  might 
be  the  case  for  electrons  if  the  nucleus  has  ten  excess 
protons,  then  there  is  some  crowding.  An  oppor- 
tunity for  two  children  to  join  an  adjacent  but  less 
crowded  circle  will  be  welcomed  by  the  children,  and 
by  the  teacher  also,  if  she  can  satisfy  her  quantita- 
tive obligations  by  supervising  their  play  in  a 
neighboring  circle. 

An  atom  with  a  circle  crowded  by  electrons  is  in 


SATISFIED  AND  UNSATISFIED  SYSTEMS:      15 

an  unsatisfied  condition  which  is  favorable  to  losing 
electrons.  If  it  does  so  it  will  have  more  protons 
than  electrons.  This  tendency  towards  an  excess  of 
protons  is  ordinarily  described  by  calling  the  atom 
electropositive.  It  can  supply  electrons  to  any  other 
atom  which  can  accommodate  them  in  its  circle.  If 
it  does  so,  however,  the  two  atoms  must  remain 
together  for  each  nucleus  has  responsibility  for  a 
definite  number  of  the  total  of  electrons.'  For  such 
a  combination  into  a  molecule  the  second  kind  of 
atom  must  have  a  complementary  need,  having 
fewer  electrons  than  can  be  satisfactorily  accommo- 
dated in  its  ring.  Its  tendency  to  acquire  added 
electrons  is  indicated  by  calling  it  electronegative. 

If  an  atom  has  a  ring  of  electrons  just  sufficient 
to  play  their  circle  game  without  crowding  there  will 
be  no  need  for  loaning  or  borrowing  from  an  adja- 
cent atom,  and  hence  no  occasion  for  combination 
into  a  molecule.  The  elements  with  atoms  of  this 
character  are  "inert"  substances  such  as  the  gases 
helium,  argon,  neon  and  krypton.  Niton  is  also  an 
example  of  such  an  arrangement.  Niton,  however, 
is  inert  only  as  far  as  concerns  its  possibility  of  com- 
bination with  other  atoms,  for,  due  to  its  radio- 
active properties,  it  can  very  markedly  influence  the 
chemical  behaviour  of  other  substances. 

So  far  as  concerns  the  combination  into  molecular 
systems  of  two  different  kinds  of  atomic  systems,  we 
should  expect  electropositive  atoms  to  unite  with 
electronegative  ones.  Common  salt,  Nad,  is  the 
combination  of  the  electropositive  sodium  atom, 
which  would  spare  one  electron,  with  the  electroneg- 


16  WITHIN  THE  ATOM 

ative  chlorine  atom,  which  would  accommodate  an 
extra  electron.  In  forming  the  molecule  the  electrons 
probably  redistribute  themselves  about  the  two 
nuclei. 

Under  certain  conditions  the  combination  so 
formed  may  be  broken  up  into  two  new  systems, 
which  are  slightly  different  from  the  original  sodium 
and  chlorine  atoms.  If  salt  is  dissolved  in  water 
some  of  its  molecules  separate  into  these  two  parts. 
One  has  the  nucleus  of  a  sodium  atom  and  the  other 
that  of  a  chlorine  atom.  The  number  of  electrons 
about  each  of  these  nuclei  is  not  that  of  the  normal 
atom.  In  the  process  of  separating,  the  electron 
which  was  borrowed  by  the  ring  about  the  chlorine 
nucleus  is  not  returned. 

The  chlorine  nucleus  and  its  ring  with  an  excess 
electron  is  not  a  chlorine  atom,  nor  is  the  sodium 
nucleus  with  its  ring,  which  has  lost  an  electron,  an 
atom  of  sodium.  When  ordinary  table  salt  breaks 
up  in  solution,  it  does  not  give  the  elementary  sub- 
stances of  sodium  and  chlorine,  neither  of  which  is  a 
possible  food.  These  new  atomic  systems  move 
about  in  the  solution  exactly  as  do  unsplit  molecules. 
To  them  is  given  a  new  name,  that  of  "ions"  since 
they  are  go-ers.  Sometimes  they  come  together  in 
their  wanderings  and  for  a  tune  form  again  a  salt 
molecule  but  later  they  may  break  apart. 

The  phenomena  of  solution  and  in  fact  all  matters 
having  to  do  with  the  motions  through  space  of 
atomic  or  molecular  systems  must  be  postponed. 
The  dissociation  of  the  molecular  system  of  sodium 
chloride  into  atomic  systems  has  been  cited  as  a  step 


SATISFIED  AND  UNSATISFIED  SYSTEMS      17 

toward  the  fuller  study  of  the  combination  of  atomic 
systems  into  molecular  systems.  When  the  sodium 
ion,  that  is  the  positive  ion,  comes  into  the  imme- 
diate neighborhood  of  the  chlorine,  that  is  the  nega- 
tive ion,  recombination  will  again  occur  although  a 
dissociation  may  immediately  follow  as  the  result 
of  those  external  influences  which  we  are  at  present 
assuming  without  explaining. 

Ions  are  atomic  systems  unsatisfied  in  quantity 
rather  than  in  configuration  of  electrical  elements. 
Combination  of  atomic  systems  into  molecular  sys- 
tems is,  therefore,  seen  to  occur  as  the  result  of 
either  type  of  unsatisf action.  For  historical  reasons 
both  of  the  kinds  of  combination,  which  we  have 
pictured  above,  are  called  chemical  combinations 
without  regard  to  our  more  recent  knowledge  that 
they  are  entirely  electrical  phenomena. 

The  ability  of  an  electropositive  atom,  for  ex- 
ample sodium,  or  of  a  negative  ion,  for  example  the 
chlorine  ion,  to  enter  into  a  molecular  combination 
depends  (as  we  have  seen)  upon  the  possession  of 
one  (or  more)  electrons  in  excess  of  those  requisite 
to  satisfaction  in  configuration  or  in  quantity,  re- 
spectively. We  may  therefore  express  the  ability  x>f 
an  atomic  system  to  combine,  which  is  conven- 
tionally termed  its  valence,  in  terms  of  the  number 
of  electrons  which  measure  its  unsatisf  action.  Thus 
we  may  say  that  the  atomic  systems  mentioned  .im- 
mediately above  have  a  positive  valence  of  one.  The 
atoms  or  ions  which  become  the  partners  in  such 
combinations  have  a  complementary  need  of  elec- 


18  WITHIN  THE  ATOM 

irons.  They  may  be  described  as  having  a  negative 
valence  of  one. 

For  a  satisfied  system,  that  is  for  an  inert  atom, 
the  valence  is,  of  course,  zero. 

The  satisfaction  of  that  need  on  the  part  of  an 
atomic  system  which  is  expressed  quantitatively  by 
its  valence  may  be  obtained  in  a  number  of  ways.  A 
monovalent  atomic  system  like  sodium  requires  only 
another  monovalent  system,  like  chlorine,  which  has 
a  complementary  need  to  form  a  satisfied  molecular 
structure.  A  divalent  atom,  on  the  other  hand,  may 
be  satisfied  by  a  union  with  another  divalent  atom 
or  with  two  monovalent  atoms.  In  the  latter  case 
the  two  necessary  atoms  may  be  of  the  same  kind 
or  different.  In  the  molecular  system  oj:  water  the 
divalent  oxygen  atom  is  combined  with  two  similar 
monovalent  hydrogen  atoms.  The  symbol  H20,  in 
which  the  subscript  indicates  the  number  of  atoms 
of  the  type  to  which  it  is  affixed,  is  a  convenient 
representation  of  this  combination.  In  similar  man- 
ner the  molecular  system  formed  by  the  divalent 
oxygen  atom  with  two  unlike  atoms  of  sodium  and 
hydrogen  is  symbolized  as  NaOH. 

Many  atomic  structures  attain  satisfaction  by 
combining  into  molecular  form  with  others  of  their 
own  type.  Thus  hydrogen  normally  exists  in  a 
diatomic  molecular  state  represented  as  H2.  The 
same  is  true  of  oxygen  which  forms  a  molecular  sys- 
tem of  O2.  In  such  cases  we  find  a  combination  of 
two  atomic  systems  with  similar  rather  than  comple- 
mentary needs.  The  rearrangement  of  the  electrons 
about  the  two  nuclei,  apparently,  results  in  a  more 


SATISFIED  AND  UNSATISFIED  SYSTEMS      19 

stable  configuration  than  exists  in  the  individual 
atomic  structures  although  sometimes  not  as  stable 
as  it  might  be.  A  spark  will  explode  a  mixture  of 
hydrogen  and  oxygen  and  result  in  two  molecules  of 
water  being  formed  from  one  molecule  of  oxygen  and 
two  molecules  of  hydrogen.  The  operation  is  con- 
veniently symbolized  as  02  +  2H2  — >  2H2O. 

The  atomic  system  of  oxygen  is  the  great  joiner 
and  has  fraternal  relations  with  all  except  the  most 
deadly  dull  and  inert  atoms.1  It  belongs  to  thou- 
sands of  complex  molecular  societies.  Associated 
with  hydrogen  it  enters  as  water  of  crystallization 
into  secret  organizations  of  molecules  of  which  it  is 
not  a  bona  fide  member  but  from  which  it  may  be 
expelled  only  by  heated  action.  Even  then  all  the 
water  molecules  do  not  leave  with  equal  readiness 
for  some  resist  expulsion  with  considerable  tenacity. 

It  was  largely  by  a  study  of  combinations  of  oxygen 
with  nitrogen  that  Dalton  arrived  at  his  well  known 
laws  as  to  molecular  composition.  The  substance  of 
these  laws  has  been  tacitly  assumed  in  our  earlier 
discussion.  The  unit  in  chemical  combinations  is 
the  atomic  system;  and  molecular  systems  are 
formed  only  from  whole  numbers  of  atomic  systems. 

1  And  fluorine. 


CHAPTER  III 

THE  PERIODIC  TABLE  OF  ATOMIC  SYSTEMS 

AN  atomic  system  is  formed  by  a  nucleus  and  a 
number  of  electrons  external  to  it.  In  the  configura- 
tion of  these  external  electrons  is  to  be  found  the 
secret  of  the  ability  of  one  atomic  system  to  combine 
with  one  or  more  other  systems  to  form  a  molecular 
system.  The  valence,  which  measures  this  ability 
to  combine,  may  be  positive  or  negative  depending 
upon  whether  the  system  under  consideration  is  un- 
satisfied as  the  result  of  too  many  or  of  too  few 
electrons  for  a  stable  configuration  of  the  external 
electrons. 

In  the  nucleus  there  is  always  an  excess  of  protons 
and  the  number  by  which  this  excess  is  specified  is 
known  as  the  atomic  number.  The  largest  known 
atomic  number  is  92.  On  the  basis  of  atomic  num- 
bers, therefore,  a  classification  may  be  established  of 
92  types  of  atomic  systems.  These  types  may  then 
be  cross-classified  on  the  basis  of  valence. 

As  we  proceed  from  one  type  of  atomic  system 
to  that  with  the  next  atomic  number  there  is  a 
change  of  one  in  the  number  of  excess  protons  in 
the  nucleus  and  a  corresponding  change  of  one  in  the 
number  of  external  electrons.  For  example,  let  us 
enter  our  system  of  classification  by  atomic  numbers 

20 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS     21 

at  the  eleventh  type,  which  is  that  of  the  sodium 
atom.  We  must  picture  this  atomic  system  with 
eleven  excess  protons  in  the  nucleus  and  eleven  ex- 
ternal electrons,  the  actual  configuration  of  which 
is  still  problematical.  Despite  the  fact  that  there 
is  a  quantitative  balance  between  the  protons  and 
the  electrons,  of  complementary  properties,  there  is 
a  lack  of  satisfaction  in  the  portion  of  the  system 
comprised  by  the  external  electrons. 

In  the  system  of  next  smaller  number  there  are 
ten  external  electrons;  and  with  the  reduction  in 
number  the  unsatisfaction  has  disappeared,  for  the 
tenth  typical  system  is  that  of  neon,  an  inert  atom. 
The  equivalence  of  number  of  protons  and  electrons 
still  remains  for  both  kinds  of  electrical  elements 
have  undergone  the  same  reduction  in  number.  The 
external  electrons,  however,  no  longer  crowd  each 
other. 

What  would  one  naturally  expect  as  the  atomic 
number  is  further  reduced?  Eleven  electrons  crowd, 
ten  do  not,  but  nine  are  too  few  for  satisfaction  of 
the  requirement  of  stability.  The  atomic  system 
of  the  ninth  type,  known  as  fluorine,  despite  its 
quantitative  satisfaction,  is  unsatisfied  in  configura- 
tion by  one  electron.  Like  the  sodium  system  it 
also  has  a  valence  of  unity  but  negative  instead  of 
positive. 

The  satisfied  atomic  system  is  thus  seen  to  occur 
as  a  transition  between  systems  of  negative  and  posi- 
tive valence.  Such  transitions  occur  at  the  atomic 
systems  of  helium,  neon,  argon,  krypton,  xenon,  and 
niton  for  which  the  atomic  numbers  are  respectively, 


22  WITHIN  THE  ATOM 

2,  10,  18,  36,  54  and  86.  For  convenience  the  names 
of  the  various  types  of  systems  corresponding  to  the 
atomic  numbers  below  22  are  given  in  the  accom- 
panying table. 

TABLE  I 
THE  NAMES  AND  NUMBERS  OF  THE  ATOMIC  SYSTEMS 

1  Hydrogen    H  12  Magnesium    Mg 

2  Helium*    He  13  Aluminum    Al 

3  Lithium    Li  14  Silicon    Si 

4  Beryllium    Be  15  Phosphorus    P 

5  Boron    B  16  Sulphur    S 

6  Carbon    C  17  Chlorine    Cl 

7  Nitrogen    N  18  Argon*    A 

8  Oxygen    O  19  Potassium    K 

9  Fluorine    Fl  20  Calcium    Ca 

10  Neon*     Ne  21    Scandium    Sc 

11  Sodium    Na  22    Titanium    Ti 

*  Transition  system 

The  atomic  system  for  which  the  atomic  number 
is  one  less  than  that  of  a  transition  system  has  a 
negative  valence  of  one,  and  the  system  of  the  next 
greater  number  has  a  positive  valence  of  one  as  in 
the  case  just  mentioned  of  the  sequence  fluorine, 
neon,  and  sodium.  Progressing  toward  higher  num- 
bers the  positive  valence  increases,  and  toward  lower 
atomic  numbers  the  negative  valence.  In  progress- 
ing from  one  satisfied  system  to  the  next  as,  for 
example,  from  neon  to  argon,  there  must  therefore 
be  another  kind  of  transition  from  negative  valence 
to  positive.  Between  these  satisfied  systems  there 
are  three  types  with  positive  valence  of  one,  two 
and  three,  respectively,  namely,  sodium,  magnesium, 
and  aluminium,  and  three  types,  namely,  chlorine, 
sulphur  and  phosphorus,  with  the  corresponding 
values  of  negative  valence. 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS      23 

The  middle  system  of  the  sequence,  which  we  are 
considering,  is  like  a  hostess  who  is  planning  a  din- 
ner. Shall  she  invite  four  more  guests  or  four  less? 
The  decision  will  depend  upon  circumstances,  that  is 
upon  who  the  guests  are  to  be,  but  the  number  she 
will  add  or  scratch  from  her  list  is  preferably  four, 
since  that  will  make  a  satisfactory  grouping.  Some- 
times she  makes  one  choice  and  again  the  opposite 
choice  and  the  same  is  true  of  the  atomic  system 
of  silicon.  Its  valence  is  four  but  it  is  amphoteric 
for  it  partakes  of  the  character  of  both  electroposi- 
tive and  electronegative  elements. 

The  simile  of  the  hostess,  however,  is  inadequate, 
because  the  electrons  are  disposed  about  the  nucleus 
in  a  space  of  three  dimensions.  The  pictures  of  their 
disposition,  which  have  been  proposed  from  time  to 
time,  are  all  incomplete  and  none  has  been  gen- 
erally accepted  by  scientists.  The  successful  picture 
must  account  for  the  known  facts  of  chemistry  and 
also  for  those  facts  of  physics  which  relate  to  the 
radiation  of  light  from  atomic  structures.  The  maxi- 
mum number  of  electrons  which  may  be  concerned  in 
atomic  phenomena  is,  of  course,  definitely  known 
since  the  atomic  numbers  are  well  substantiated 
facts.  The  grouping  of  these  electrons,  however,  is 
still  in  the  stage  of  hypothesis  and  the  picture  which 
will  now  be  given  is  merely  that  which  today  most 
satisfactorily  accounts  for  the  largest  number  of  the 
known  phenomena. 

We  imagine *  that  the  electrons  are  disposed  about 
the  nucleus  as  if  they  lay  in  the  shells  of  one  of  those 

1  According  to  Lewis  and  Langmuir. 


24  '       /  WITHIN  THE  ATOM 

Chinese  toys  which  consists  of  a  concentric  series  of 
wooden  egg-shaped  shells.  Let  the  innermost  egg 
represent  the  nucleus.  In  the  next  or  first  shell  there 
may  be  one  or  two  electrons,  one  in  the  case  of  hydro- 
gen and  two  in  that  of  helium.  The  latter  condition 
would  obviously  admit  of  a  stable  structure  in  which 
electrons  on  diametrically  opposite  sides  of  the 
nucleus  were  held  in  the  system,  because  they  trac- 
tate with  this  nucleus,  despite  the  fact  that  they 
pellate  with  each  other.  Because  of  this  electrical 
stability,  the  atomic  system  of  helium  is  inert. 

Except  for  the  hydrogen  system  all  atomic  struc- 
tures have  these  two  electrons.  The  unsymmetrical 
configuration  of  the  hydrogen  system  accounts  for  its 
extreme  activity  as  a  chemical  element,  and  also  for 
its  formation  of  diatomic  molecules  of  hydrogen  gas. 

When  an  atomic  system  contains  more  than  two 
external  electrons,  all  electrons  in  excess  of  two  are 
disposed  on  shells  external  to  that  which  was  just 
described.  The  next  outer  shell  is  believed  to  be 
twice  as  far  from  the  nucleus,  and  hence  to  have  four 
times  the  superficial  area.  In  it  a  total  of  eight 
electrons  may  be  located. 

The  atomic  system  which  has  one  electron  in  this 
second  shell  is  that  of  lithium.  This  atom  readily 
parts  with  its  third  electron  and  assumes  the  more 
stable  configuration  of  the  helium  atom.  That  is 
what  takes  place  when  the  molecular  system  of 
lithium  chloride,  LiCl,  dissociates  into  a  lithium  ion 
and  a  chlorine  ion.  Geometrically  a  lithium  ion  is 
similar  to  the  stable  helium  atom,  but  it  does  not 
act  at  all  similarly  because  the  nucleus  of  lithium 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS     25 

has  three  excess  protons  instead  of  the  two  of  helium. 

With  two  electrons  in  the  second  shell  the  atomic 
system  is  that  of  beryllium  which  has  a  positive 
valence  of  two  since  it  takes  the  loss  of  two  electrons 
to  convert  it  into  the  stable  configuration  of  the 
helium  system.  Boron  is  a  system  with  three  elec- 
trons in  this  shell.  When  the  number  is  four,  there 
is  reached  the  important  system  of  carbon  which 
enters  into  all  organic  compounds.  Its  four  external 
electrons  in  pellating  with  each  other  probably  take 
places  such  as  to  form  the  corners  of  a  solid  figure 
of  four  equal  sides.  Nitrogen  has  five,  oxygen  six, 
fluorine  seven,  and  neon  eight  electrons  in  this 
second  layer.  In  the  last  case  the  electrons  will  dis- 
tribute themselves  four  on  each  hemisphere,  so  that 
they  form  the  corners  of  a  cube  at  the  center  of 
which  is  the  inner  shell  with  its  two  electrons  and 
within  this  the  nucleus.  The  inertness  of  the  neon 
atom  is  well  accounted  for  by  this  symmetrical  and 
stable  arrangement  of  external  electrons. 

The  system  of  fluorine  with  its  seven  electrons  in 
the  second  shell  may  be  considered  either  as  having 
seven  too  many  for  such  stability  as  is  possessed  by 
the  helium  system,  or  one  too  few  for  the  stability 
of  the  neon  system.  In  other  words,  it  has  either  a 
positive  valence  of  seven  or  a  negative  valence  of 
one.  Oxygen  has  six  and  two  respectively.  The  re- 
arrangement which  is  required  to  make  these  sys- 
tems stable,  that  is  satisfied  in  configuration,  is  less 
if  electrons  are  added  than  if  they  are  subtracted,  so 
that  such  systems  tend  in  combination  to  attain 
their  satisfaction  by  borrowing  from  the  other  com- 


26  WITHIN  THE  ATOM 

ponents  of  the  molecular  systems  in  which  they  are 
associated. 

In  the  dissociation  of  such  molecular  systems  the 
atom  tends  to  retain  its  satisfaction  by  a  failure  to 
return  the  borrowed  electron  which  amounts  to  an 
actual  theft.  Dissociation,  therefore,  results  in  the 
formation  of  negative  ions,  that  is  those  with  a  quan- 
titative excess  of  electrons. 

In  a  large  number  of  cases  of  molecular  systems 
the  electrons  are  shared  so  that  borrowing  and  theft 
do  not  occur.  It  seems  probable,  however,  that  in- 
dividual electrons  may  not  be  shared  but  only  pairs 
of  electrons.1  It  is  further  believed  that  in  the  shar- 
ing of  pairs  of  electrons  the  adjacent  atomic  groups 
so  combine  as  to  form  as  nearly  as  possible  stable 
arrangements  roughly  similar  to  that  of  the  neon 
atom,  that  is  groups  of  electrons  at  the  eight  corners 
of  a  cube,  at  the  center  of  which  is  a  kernel  com- 
posed of  two  electrons  and  a  nucleus.  This  hypo- 
thetical process  is  peculiarly  adapted  to  explain,  for 
example,  the  large  number  of  compounds  which  are 
formed  by  oxygen  with  nitrogen. 

As  the  number  of  external  electrons  is  increased 
beyond  ten  a  new  outer  shell  is  required.  Let  us 
picture  this  third  shell  as  practically  coincident  with 
the  second.  The  first  electron  to  be  disposed  in  it 
occupies  a  position  with  much  the  same  precarious- 

1  Chlorine,  which  forms  a  diatomic  molecule,  C12,  is  a  good 
illustration  of  the  sharing  of  electrons  between  the  atoms  of 
molecular  systems.  Each  chlorine  atom  lacks  one  electron  of 
the  number  required  for  satisfaction  in  configuration.  Hence, 
each  atom  shares  one  of  its  electrons  with  the  other  atom  of  its 
molecule.  The  requirements  of  configuration  are  thus  satisfied, 
and  in  effect  a  pair  of  electrons  is  shared. 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS     27 

ness  as  did  the  first  electron  of  the  second  shell,  and 
hence,  sodium,  the  eleventh  system,  has  much  the 
same  properties  as  lithium,  the  third. 

For  similar  reasons  there  is  a  periodic  recurrence 
of  the  properties  of  beryllium  when  we  reach  the 
twelfth  system,  that  is  magnesium,  and  correspond- 
ing recurrences  until  we  reach  argon,  where  the  shell 
has  its  complement  of  eight  electrons.  Again  we 
have  a  stable  structure. 

A  new  shell,  a  fourth,  is  required  for  electrons  in 
excess  of  eighteen.  This  may  not  be  superimposed, 
as  was  the  third  shell  upon  the  second,  for  these 
inner  shells  now  hold  too  many  electrons  to  permit 
so  near  a  position  for  additional  electrons.  The 
fourth  shell  is  presumably  three  times  as  far  from 
the  nucleus  as  is  the  first  and  hence  its  area  is  nine 
times  as  great  and  its  capacity  for  electrons  eighteen 
instead  of  two. 

The  first  three  of  the  atomic  systems  which  are 
formed  by  the  addition  of  electrons  in  this  new  shell 
also  partake  of  the  properties  of  the  corresponding 
three  in  the  two  series  previously  considered.  The 
area  of  the  fourth  shell  is  larger,  however,  and  it  is 
not  filled  until  eighteen  electrons  are  in  it.  The 
atomic  system  which  exists  when  this  fourth  shell 
has  four  electrons  has  no  such  amphoteric  properties 
as  have  silicon  and  carbon.  It  has  no  choice  in  its 
method  of  obtaining  stability  since  to  progress  to 
stability  would  require  the  addition  of  fourteen  elec- 
trons, while  to  regress  would  require  only  the  loss 
of  four.  Similarly  the  next  atomic  system,  with  five 
electrons  in  this  shell,  can  have  only  a  positive 


28  WITHIN  THE  ATOM 

valence.  To  assume  the  nearest  stable  structure, 
that  of  argon,  would  require  the  subtraction  of  all 
five  electrons. 

Here  we  are  met  by  a  choice  of  kinds  of  satisfac- 
tions. A  satisfaction  of  configuration  requires  the 
loss  of  five  electrons.  As  each  electron  is  lost  the 
unsatisfaction  as  to  the  discrepancy  between  num- 
bers of  protons  and  of  electrons  becomes  more 
marked.  As  long  as  a  net  balance  of  satisfaction  is 
attained  by  losing  electrons  there  will  be  a  tendency 
to  do  so.  This  balance  of  desires  is  generally  met 
before  all  five  are  lost,  for  two  and  three  are  the  usual 
valences  of  the  vanadium  system  which  we  are  con- 
sidering. 

TABLE  II 

THE  NAMES  AND  NUMBERS  OF  THE  ATOMIC  SYSTEMS 

18  Argon*    A  37  Rubidium    Rb 

19  Potassium    K  38  Strontium    Sr 

20  Calcium    Ca  39  Yttrium    Y 

21  Scandium    Sc  40  Zirconium    Zr 

22  Titanium    Ti  41  Niobium    Nb 

23  Vanadium    V  42  Molybdenum    Mo 

24  Chronium     Cr  43 

25  Manganese    Mn  44  Ruthenium    Ru 

26  Iron    Fe  45  Rhodium    Rh 

27  Cobalt    Co  46  Palladium     Pd 

28  Nickel    Ni  47  Silver    Ag 

29  Copper    Cu  48  Cadmium    Cd 

30  Zinc    Zn  49  Indium    In 

31  ,  Gallium    Ga  50    Tin    Sn 

32  Germanium    Ge  51  Antimony    Sb 

33  Arsenic    As  52  Tellurium    Te 

34  Selenium    Se  53  Iodine    I 

35  Bromine    Br  54  Xenon*    X 

36  Krypton*    Kr 

*  Transition  system 

The  names  of  the  atomic  systems  with  numbers 
between  18  and  54  are  given  in  Table  II.    From  this 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS     29 

it  will  be  seen  that  the  systems  corresponding  to 
those  with  8,  9,  and  10  electrons  in  the  fourth  shell, 
namely,  those  of  atomic  numbers  from  26  to  28,  are 
those  of  iron,  cobalt,  and  nickel,  the  three  elements 
commonly  known  as  magnetic.  They  constitute  a 
family  of  elements  with  much  in  common  besides 
their  magnetic  property.  Although  they  have  about 
half  as  many  electrons  in  their  outer  shells  as  is 
required  for  stability  they  have  a  sufficient  number 
to  form  fairly  symmetrical  systems.  Thus  iron  with 
eight  electrons  might  have  them  disposed  at  the 
corners  of  a  cube  like  that  of  the  outer  shell  in  neon 
or  argon.  Nickel  also  may  attain  considerable 
stability  with  its  ten  electrons.  Their  valences,  how- 
ever, would  not  be  zero  for  the  shells  are  incom- 
pletely filled. 

These  substances  are  not  inert  and  yet  they 
possess  certain  structural  advantages  over  their 
neighboring  systems  sufficient  to  form  an  oppor- 
tunistic goal,  toward  which  these  other  systems  may 
struggle  in  their  quest  of  satisfaction  in  form.  For 
this  reason  some  of  the  systems  on  both  sides  of 
this  group  partake  somewhat  of  their  qualities.  For 
this  reason  also,  starting  with  the  copper  system, 
which  is  next  higher  than  nickel,  the  valences  again 
form  an  ascending  series,  being  one  (or  two  in  some 
cases)  for  copper,  two  for  zinc,  three  for  gallium,  and 
four  for  the  amphoteric  germanium. 

Beyond  germanium,  where  the  shell  lacks  only 
four  electrons  of  its  complement,  satisfaction  is  most 
easily  obtained  by  adding  electrons  and  attaining  to 
the  form  of  the  inert,  stable  system  of  krypton  (36). 


30         ;,  WITHIN  THE  ATOM 

The  elements  from  arsenic  (33)  to  bromine  (35) 
correspond,  therefore,  to  those  immediately  below 
the  other  inert  elements  of  neon  and  argon.  Thus 
bromine  belongs  to  the  same  family  and  reacts  in 
the  same  general  way  to  its  electronic  surroundings 
as  do  chlorine  (17)  and  fluorine  (9). 

In  a  similar  manner  the  elements  rubidium  (37), 
strontium  (38)  and  yttrium  (39),  which  have  atomic 
numbers  immediately  above  that  of  krypton,  tend 
to  revert  in  configuration  to  that  structure  and  thus 
to  lose  electrons  just  as  do  the  corresponding  systems 
of  the  preceding  series,  namely,  potassium  (19), 
calcium  (20),  and  scandium  (21). 

Between  the  atomic  numbers  of  40  and  50  the  gen- 
eral characteristics  of  the  atomic  systems  correspond 
to  those  of  the  previous  series  for  which  the  numbers 
are  22  to  32.  Again  we  find  the  structures  of  higher 
number  tending  to  reach  satisfaction  in  configuration 
by  assuming  that  of  the  next  highest  stable  system. 
Thus  iodine,  the  fifty-third  system,  would  attain 
satisfaction  in  gaining  an  electron  and  becoming  in 
form  like  xenon,  the  fifty-fourth,  in  the  same  man- 
ner as  chlorine,  the  seventeenth,  would  assume  the 
form  if  not  the  substance  of  argon,  the  eighteenth 
system. 

Beyond  xenon  the  names  of  the  atomic  systems 
are  given  in  Table  III.  A  new  shell  is  now  required 
and  we  imagine  one  with  four  times  the  diameter  of 
the  first,  sixteen  times  its  area,  and  a  capacity  for 
thirty-two  electrons.  The  first  six  elements  in  this 
new  series  correspond  to  the  first  six  hi  the  two  im- 
mediately previous  series.  The  seventh,  of  atomic 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS     31 

number  61,  is  as  yet  undiscovered.  Of  the  last  seven, 
the  one  with  an  atomic  number  of  85  is  also  undis- 
covered. Otherwise  the  higher  elements  of  this  series 
are  like  those  immediately  below  the  transition  sys- 
tems of  xenon  and  krypton. 

TABLE  III 
THE  NAMES  AND  NUMBERS  OF  THE  ATOMIC  SYSTEM 

54  Xenon*    X  74  Tungsten    W 

55  Cesium     Cs  75  

56  Barium    Ba  76  Osmium    Os 

57  Lanthanum     La  77  Iridium    Ir 

58  Cerium    Ce  78  Platinum    Pt 

59  Praseodymium    Pr  79  Gold    Au 

60  Neodymium    Nd  80  Mercury    Hg 

61    81     Thallium     Tl 

62  Samarium    Sa  82  Lead    Pb 

63  Europium     Eu  83  Bismuth    Bi 

64  Gadolinium    Ga  84  Polonium    Po 

65  Terbium    Tb  85  

66  Dysprosium    Ds  86  Niton*    Nt 

67  Holmium     Ho  87  

68  Erbium    Er  88  Radium    Ra 

69  Thulium    Tu  89  Actinium    Ac 

70  Ytterbium    Yb  90  Thorium    Th 

71  Lutecium    Lu  91  Uranium  XH    Ur  Xn 

72    92    Uranium    Ur 

73  Tantalum   Ta 

*  Transition  systems. 

Of  the  thirty-one  atomic  systems  between  xenon 
(54)  and  niton  (86),  the  first  seven  (55-61)  corre- 
spond to  systems  (37-43)  and  (19-25).  The  last 
seven  (79-85)  correspond  in  chemical  properties  to 
systems  (47-53)  and  (29-35).  Both  the  lower  series, 
(19-35)  and  (37-53),  have  intermediate  transition 
systems  of  which  the  iron-cobalt-nickel  group  (26- 
28)  is  the  more  noteworthy.  These  intermediate 
transition  systems  are  believed  to  be  somewhat 
analogous  to  the  transition  systems  formed  by  the 


32  WITHIN  THE  ATOM 

inert  gases  in  that  they  have  fairly  stable  electronic 
configurations,  but  they  differ  by  being  chemically 
active  because  they  are  not  completely  satisfied  as 
to  configuration. 

In  the  series  which  we  are  now  considering  there 
are  two  such  intermediate  transition  groups,  namely, 
(62-64)  and  (76-78).  Of  these  the  latter,  represent- 
ing osmium,  iridium,  platinum,  is  the  more  impor- 
tant. The  other  group  contains  three  rare  earths, 
namely,  samarium  (62),  europium  (63),  and  gadoli- 
nium (64). 

Between  these  two  intermediate  groups  of  transi- 
tion systems  there  are  nine  known  and  two  unknown 
systems,  (72  and  75).  With  the  exception  of  tan- 
talum (73)  and  tungsten  (74)  these  are  all  rare 
earths — metallic  elements  with  positive  valences  of 
three.  The  pictures  of  electronic  configuration  which 
have  been  proposed  to  account  for  the  elements  be- 
tween (62)  and  (77)  are  not  as  yet  generally  ac- 
cepted and  need  not  be  discussed.  It  is  perhaps 
sufficient  to  record  the  fact  that  chemical  properties 
do  not  vary  sharply  with  increase  in  number  of 
planetary  electrons  when  the  shell  has  more  than 
eight  electrons,  but  is  not  within  eight  of  its  comple- 
ment. 

Beyond  the  last  inert  system,  that  of  niton,  there 
are  only  a  few  known  systems,  and  the  series  termi- 
nates with  uranium  from  which  by  radioactive  proc- 
esses many  of  the  lower  systems  were  undoubtedly 
derived.  These  few  remaining  systems  require  elec- 
trons in  a  seventh  shell,  which  we  imagine  to  be 


Rare, 


FlQ.   1 

Atomic  systems  at  the  periodic  table.  Place  numbers  corre- 
spond to  atomic  numbers.  Systems  similarly  situated,  as  indi- 
cated by  radial  lines,  have  similar  chemical  properties. 

33 


34  WITHIN  THE  ATOM 

superposed  upon  the  sixth  and  to  have  the  same 
capacity. 

We  may  now  make  a  schematic  picture  of  the 
series  of  atomic  structures  as  if  there  were  a  group 
of  tables  to  be  filled  by  guests.  These  tables  are 
roughly  concentric  as  shown  in  Fig.  1.  One  by  one 
the  atomic  systems  are  seated  and  the  order  of  their 
seating  is  given  by  the  atomic  numbers  attached  to 
their  places.  The  first  table  seats  only  two.  The 
next  table  eight  on  each  side.  The  third  table,  seat- 
ing eighteen  on  each  side,  must  place  some  atomic 
systems  in  positions  which  do  not  correspond  with 
any  of  those  at  the  second  table.  There  is,  however, 
a  correspondence  between  atomic  systems  which  are 
opposite  one  another  at  the  same  table.  The  fourth 
table  differs  in  some  ways  from  any  of  the  inner  ones 
and  on  one  side  it  is  only  partially  filled. 

In  this  representation  atomic  systems  which  have 
corresponding  characteristics  will  be  found  to  lie  on 
the  same  radial  line.  That  corresponding  to  the 
stable  systems  is  marked  zero.  The  others  are 
marked  with  Roman  numerals  for  the  convenience 
of  those  who  wish  to  compare  with  the  usual  tabular 
presentation  of  the  periodic  series  of  the  chemical 
elements.  Intermediate  transition  systems  are  indi- 
cated by  VIII.  To  a  very  large  extent  the  elements 
correspond  in  positive  valence  to  the  Roman  nume- 
rals, thus  the  elements  of  group  I  all  have  positive 
valences  of  one  although  copper  may  also  have  two 
and  gold  may  have  three  as  values  of  valence.  For 
groups  beyond  IV,  the  exceptions  become  more 
frequent  as  is  evident  from  Table  IV,  where  the 


PERIODIC  TABLE  OF  ATOMIC  SYSTEMS      35 


PB|     » 


*<* 


o 


Oi    ' 


a 


fcO 
0*? 


* 


PH  oo 


43  •? 


<o    „ 


8 


* 


s 


a 


v 
Wo 


§8 


So 


36  WITHIN  THE  ATOM 

periodic  series  is  tabulated.  This  table  gives  for 
each  element,  except  for  some  of  the  rare  earths,  the 
atomic  number,  the  chemical  symbol  and  the  various 
observed  valences. 


CHAPTER  IV 

MASS   AND    INERTIA   OF  ATOMIC    SYSTEMS 

THE  physical  matter  of  which  we  are  composed 
and  with  which  we  deal  whether  as  scientists  or  not 
is  composed  of  discrete  molecules  which  are  but 
unions  of  smaller  particles,  the  atomic  systems.  Of 
the  latter,  we  have  distinguished  ninety-two  types 
which  differ  in  the  number  of  excess  protons  in  their 
nuclei  and  consequently  also  in  the  number  and  con- 
figuration of  the  planetary  electrons  about  their 
nuclei.  Because  these  external  electrons  are  all  iden- 
tical, the  various  atomic  systems  form  a  progressive 
series  of  geometrical  patterns  in  which  certain 
typical  relations  periodically  recur.  The  series, 
therefore,  contains  groups  or  families  of  atomic 
types,  which  possess  similar  or  common  charac- 
teristics. 

Although  the  actual  configurations  are  not  known, 
the  hypothetical  scheme  of  disposition  for  the  planet- 
ary electrons,  which  was  presented  in  the  last  chap- 
ter, accounts  for  a  sufficiently  large  number  of  the 
known  relationships  of  atoms  to  warrant  its  tentative 
acceptance.  About  the  nucleus  the  electrons  are 
grouped  as  if  they  occupied  cells  in  shells  of  diam- 
eters which  are  related  as  1:2:2:3:3:4:4  and  of 
capacities  for  electrons,  2,  8,  8,  18,  18,  32  and  32  re- 

37 


38  WITHIN  THE  ATOM 

spectively.  No  electrons  exist  in  outer  shells  unless 
those  within  are  completely  filled.  Those  systems 
which  have  no  partially  filled  shells  are  satisfied  inert 
structures  to  whose  configuration  the  unsatisfied  sys- 
tems tend  to  revert  or  to  progress.  In  this  tendency 
is  the  proximate  cause  of  the  chemical  actions  of 
various  kinds  of  atoms. 

The  basis  which  has  been  chosen  for  the  classifica- 
tion of  atomic  systems  is  relative  in  that  it  depends 
upon  the  excess  of  protons  in  the  nucleus  over  the 
electrons  and  not  at  all  upon  the  total  number  of 
either  kind  of  electrical  element.  It  is  therefore 
possible  that  two  or  more  atomic  systems  may  exist 
which  classify  as  of  the  same  type,  that  is  are  iso- 
topic  at  the  Periodic  Table,  but  differ  in  the  total 
number  of  protons  in  their  nuclei.  In  all  chemical 
combinations  or  reactions  these  isotopes  are  indistin- 
guishable. They  may  be  distinguished,  however,  as 
the  result  of  an-  important  physical  property  of  elec- 
trical elements  which  is  most  pronounced  in  the 
case  of  protons. 

This  property  is  that  of  inertia,  the  inherent  un- 
willingness to  change  in  state  of  motion  which  is 
common  not  only  to  the  infinitesimal  elements  but 
to  such  larger  aggregations  as  compose  ponderable 
objects,  whether  human  or  otherwise.  It  is  this 
quality  which  makes  the  flying  missile  so  destructive 
and  the  stone  wall  or  conservative  so  annoying.  The 
first  delivers  a  blow  and  the  second  resists  our  force 
and  impedes  our  progress. 

Because  of  the  phenomenon  of  gravitation  we  have 
become  accustomed  to  measure  inertia  by  weight 


MASS  AND  INERTIA  OF  ATOMIC  SYSTEMS     39 

and  a  popular  misconception  ha^s  arisen  in  which 
weight,  mass  and  inertia  are  inextricably  confused. 
The  difficulty  is  largely  due  to  our  instinctive  ap- 
proach to  scientific  questions  through  our  immediate 
but  frequently  misleading  sensations. 

When  we  cause  a  body  to  alter  its  state  of  motion, 
either  by  changing  its  speed  or  its  direction,  we  are 
conscious  of  exerting  what  we  are  pleased  to  call  a 
force.  When  we  observe  the  gravitational  tractation 
of  body  and  earth  we  speak  of  a  force  of  gravitation 
as  acting  on  the  body.  Bodies  upon  which  the  earth 
under  similar  conditions  exerts  equal  forces  we  call 
equal  in  weight.  Unfortunately  weight  is  but  a  par- 
ticular kind  of  force  and  force  itself  is  an  entirely 
subjective  concept  without  any  objective  reality. 
Whatever  may  be  the  character  of  the  alteration  in 
the  relative  motions  of  the  bodies  of  a  system  the 
alteration  is  but  the  manifestation  of  a  change  in 
the  disposition  and  availability  of  that  uncompre- 
hended  motive  power  of  our  universe  which  we  call 
energy. 

Energy  and  the  electrical  elements  are  the  postu- 
lates of  the  new  science,  the  entities  in  terms  of 
which  all  explanations  of  scientific  phenomena  must 
be  made. 

To  our  senses,  whether  aided  by  apparatus  or  not, 
this  motive  power,  or  energy,  is  evidenced  only  by 
changes  in  the  state  of  motion  of  the  electrical  ele- 
ments. To  every  moving  particle,  whether  electron, 
proton,  atom,  molecule,  or  more  evident  mass,  we 
ascribe  a  portion  of  this  unknown.  The  amount 
which  we  assign  to  any  particle  depends  upon  the 


40  WITHIN  THE  ATOM 

speed  with  which  it  is  moving  and  upon  its  electrical 
composition. 

As  the  unit  by  which  to  measure  energy  we  may 
take  that  energy  which  is  associated  with  an  electron 
under  some  definite  and  arbitrarily  chosen  condition 
of  motion.  For  example,  we  might  choose  the  speed 
of  one  centimeter  a  second  as  that  at  which  an 
electron  would  be  traveling  when  it  had  what  we 
wish  to  call  a  unit  amount  of  energy.  Two  electrons 
moving  with  this  speed,  obviously,  represent  two 
units  of  energy. 

When  two  bodies  differ  in  kinetic  energy x  even 
though  their  speeds  are  alike  we  say  that  they  differ 
in  inertia  or  hi  mass.  In  quantitative  significance 
the  two  terms  are  interchangeable  although  the  first 
represents  the  unwillingness  of  a  body  to  change  its 
state  of  motion  and  the  second  the  quantity  of  mat- 
ter in  the  body.  On  the  basis,  for  example,  of  experi- 
mental observations  of  the  relation  for  the  energies 
of  any  body  and  of  an  electron  we  may  ascribe  to 
the  body  a  mass  which  is  some  definite  number  of 
times  that  of  an  electron. 

If  we  are  to  express  quantitative  relationships  we 
shall  need  units.  Three  fundamental  units  are  all 
that  are  required  and  these  have  already  been 
chosen.  They  are  the  units  of  distance,  time,  and 
energy.  Our  unit  magnitudes  are  then  the  centi- 
meter, the  second,  and  the  kinetic  energy  of  an  elec- 
tron which  is  moving  one  centimeter  per  second. 

The  habit  of  reducing  all  quantitative  expressions 

"That  is,  energy  associated  with  a  body  as  consequence  of  its 
motion. 


MASS  AND  INERTIA  OF  ATOMIC  SYSTEMS     41 

to  terms  of  a  very  limited  number  of  units  is  not  re- 
stricted to  scientific  procedure  but  holds  in  many 
other  human  activities.  To  a  large  extent  we 
measure  our  desires  and  their  gratification  in  terms 
of  the  distance  we  would  go,  the  time  we  would 
consume,  and  the  money  we  would  expend. 

There  is  a  wide  range  of  choice  in  the  selection  of 
magnitudes  upon  which  to  base  three  fundamental 
units,  but  for  present  purposes  the  three  previously 
mentioned  are  to  be  preferred.  In  terms  of  these 
we  may  define  unit  mass.  First,  however,  we  recog- 
nize that  a  speed  of  one  centimeter  per  second  is  a 
speed  of  unit  distance  in  unit  time,  that  is  a  speed 
of  unity.  Double  the  distance  in  the  same  tune  or 
the  same  distance  in  half  the  time  represents  a  speed 
of  two  units.  In  terms  of  units  of  speed  we  now 
see  that  our  chosen  unit  of  energy  is  that  associated 
with  an  electron  which  is  moving  with  unit  speed. 
The  next  step  is  to  define  unit  mass  as  that  of  a  body 
which  has  unit  energy  when  its  speed  is  unity. 

It  is  to  be  noted  against  future  reference  that  this 
definition  carries  no  implication  as  to  the  constancy 
of  mass  and  contains  no  indications  as  to  the  rela- 
tionship of  mass,  speed,  and  energy.1  The  considera- 
tion of  these  matters  may  be  omitted  since  our  im- 
mediate discussion  requires  only  the  recognition  of 
mass  as  a  factor  for  expressing  the  relation  of  the 
energies  of  two  bodies  whose  speeds  are  identical. 

We  assume  that  energies  are  determinable  and 
that  speed  is  not  only  measurable  but  controllable 
so  that  we  may  determine  the  mass  of  a  body  by 

1  For  such  a  relation  cf.  p.  205  in  the  Appendix. 


42  WITHIN  THE  ATOM 

finding  its  energy  at  unit  speed.  When  so  deter- 
mined the  mass  of  an  alpha  particle  is  7380  times 
that  of  the  electron.  The  alpha  particle,  however, 
is  merely  the  nucleus  of  the  atomic  system  known 
as  helium.  When  associated  with  two  planetary  elec- 
trons it  becomes  an  atom  of  helium.  The  mass  of 
the  atomic  system  of  helium,  therefore,  is  due  almost 
entirely  to  this  nucleus. 

Alpha  particles  are  known  to  be  constituents  of 
the  nuclei  of  all  radioactive  atomic  systems  and  are 
assumed  to  be  present  in  all  other  systems  except 
hydrogen.  It  seems  highly  probable,  therefore,  that 
within  the  nucleus  of  any  atomic  structure  the  pro- 
tons are  associated  in  groups  of  four,  bound  together 
with  two  electrons  in  the  same  manner  as  in  the 
alpha  particle.  Whenever  the  number  of  protons 
in  the  nucleus  is  divisible  by  four  we  may,  therefore, 
expect,  although  we  do  not  yet  know,  that  the 
nucleus  is  formed  by  an  integral  number  of  alpha 
particles. 

Consider,  for  example,  such  a  nucleus  as  would  be 
formed  by  four  alpha  particles.  Each  constituent 
contributes  four  protons  and  two  electrons  so  that 
the  nucleus  contains  a  total  of  sixteen  protons  and 
eight  electrons.  Its  atomic  number  would  then  be 
eight,  that  is,  its  construction  would  correspond  in 
valence  and  in  other  chemical  properties  to  the  atom 
of  oxygen.  Its  mass  would  be  due  to  four  alpha 
particles  and  would  be  four  tunes  that  of  the  helium 
atom,  and  this,  in  fact,  is  the  experimentally  deter- 
mined ratio  for  the  masses  of  the  oxygen  and  helium 
atoms. 


MASS  AND  INERTIA  OF  ATOMIC  SYSTEMS     43 

A  nuclear  composition  of  only  alpha  particles  is 
not  possible,  however,  where  twice  the  atomic  num- 
ber is  not  evenly  divisible  by  four.  In  such  cases  we 
must  assume  the  nucleus  to  contain l  in  addition  to 
alpha  particles  one  or  more  protons.  In  the  case 
of  nitrogen,  for  example,  it  has  been  determined  re- 
cently that  protons  are  part  of  the  nucleus  for  they 
may  be  knocked  out  from  the  nuclei  of  nitrogen 
atoms  by  impacts  from  other  atomic  systems  which 
are  moving  with  enormous  speeds. 

In  determining  the  mass  of  an  atom  we  may 
neglect  the  electrons  and  assume  that  each  proton 
contributes  to  the  nucleus  one-quarter  of  the  mass 
of  an  alpha  particle.  For  any  nucleus,  then,  we  may 
calculate  the  mass  as  some  improper  fraction  of  the 
mass  of  an  alpha  particle.  For  example,  if  an  atomic 
system  has  twenty-two  protons  in  its  nucleus  it  has 
a  mass  of  22/4ths  of  an  alpha  particle.  We  may 
compare  the  mass  also  to  that  of  an  atom  of  oxygen. 
Since  the  latter  is  four  times  as  heavy  as  the  helium 
atom,  the  mass  of  the  system  which  we  are  consid- 
ering is  22/16ths  that  of  an  oxygen  atom.  In  addi- 
tion to  the  system  with  twenty-two  protons  let  us 
assume  another  which  has  twenty  protons.  Its  mass 
will  be  20/16ths  that  of  an  oxygen  atom.  Instead 
of  working  with  fractions  we  shall  let  16  stand  for 
the  mass  of  an  atom  of  oxygen  and  then  in  terms 
of  the  new  unit  thus  arbitrarily  adopted  we  may  ex- 
press the  masses  of  the  hypothetical  systems  as  22 
and  20  respectively. 

So  far  we  have  been  concerned  only  with  their 

*C/.  footnote  of  p.  114,  and  also  p.  111. 


44  WITHIN  THE  ATOM 

masses.  Now  let  us  assume  that  they  are  of  the 
same  type,  each  with  an  atomic  number  of  ten.  The 
configuration  of  the  ten  planetary  electrons  will  then 
be  the  same  in  both  structures;  the  valence  will  be 
the  same;  the  chemical  properties  will  be  the  same; 
and  the  only  difference  will  be  in  mass.  The 
isotopes,  which  we  are  imagining,  cannot  be  sepa- 
rated by  chemical  methods  for  they  have  identical 
behaviours  in  all  reactions. 

Let  us  further  suppose  that  this  chemical  identity 
has  resulted  during  the  ages  past  in  such  a  mixing  of 
these  isotopes  that  wherever  one  obtains  a  sample  of 
this  chemical  element  the  sample  will  contain  them 
in  the  same  proportion.  Suppose,  for  example,  that 
there  are  nine  atoms  of  the  isotope  with  mass  20  for 
every  one  of  that  with  mass  22.  Any  determination 
of  the  atomic  mass  will  give  the  average  mass,  that  is 
20.2,  since  on  the  average  the  total  mass  of  ten  atoms 
would  be  9X20+1X22  or  202. 

We  now  turn  to  Table  V  in  which  are  given  for 
some  of  the  chemical  elements  their  so-called  atomic 
weights,  on  the  basis  of  16  for  the  oxygen  atom. 
For  neon,  which  we  know  to  have  an  atomic  number 
of  ten,  the  atomic  weight  is  20.2.  The  gas  which  the 
chemists  used  to  know  as  neon  is  not  a  homogeneous 
gas,  composed  of  identical  atoms,  but  is  a  mixture  of 
two  gases,  the  atoms  of  which  are  alike  in  atomic 
number  but  unlike  in  mass. 

These  two  isotopes,  of  atomic  weights  20  and  22, 
have  recently  been  isolated  by  physical  rather  than 
chemical  methods.  The  methods  used  are  made 
possible  by  the  fact  that  systems  which  differ  in  mass 


MASS  AND  INERTIA  OF  ATOMIC  SYSTEMS     45 

will  have  different  energy  contents  at  the  same  speed. 
As  we  shall  see  later,  however,  the  actual  experi- 
mental determinations  are  based  on  the  converse 
statement  of  this  relationship ;  if  two  particles  of  dif- 
ferent masses  are  given  equal  energies  they  will  differ 
in  speed,  the  smaller  mass  attaining  the  greater 
speed. 
The  table  of  atomic  weights,  to  which  reference 

TABLE  V 
ATOMIC  WEIGHTS  OF  SOME  COMMON  CHEMICAL  ELEMENTS 

Hydrogen    1.008  Copper 63.57 

Helium    4.00  Zinc    65.37 

Lithium   6.94  Arsenic 74.96 

Beryllium 9.1  Selenium    79.2 

Boron   11.0  Bromine    79.92 

Carbon  12.0  Krypton 82.92 

Nitrogen    14.01  Rubidium 85.45 

Oxygen    16.0  Palladium    106.5 

Fluorine  19.0  Silver 107.88 

Neon   20.2  Cadmium  112.4 

Sodium    23.00  Tin    118.7 

Magnesium  24.32  Antimony    120.2 

Aluminum  27.1  Iodine    126.92 

Silicon    28.3  Xenon    130.2 

Phosphorus 31.05  Caesium    132.81 

Sulphur    32.06  Barium    137.4 

Chlorine    35.45  Tungsten  184. 

Argon   39.9  Osmium   190.9 

Potassium   39.10  Iridium    193.1 

Calcium   40.1  Platinum  195.2 

Manganese    54.93  Gold   197.2 

Iron    55.84  Mercury    200.6 

Nickel - 58.68  Lead  207.2 

Cobalt 58.97  Bismuth  208.0 

NOTE:     The  following  elements  have  isotopes  of  the  following 
atomic  masses: 

Lithium,  6,  7  Bromine  79,  81 

Boron,  10,  11  Rubidium  85,  87 

Neon  20,  22  Krypton  84,  86,  82,  83,  80,  78 

Magnesium  24,  25  Xenon  128,  130,  131,  133,  135 

Silicon  28,  29  Mercury  (197-200),  202,  204 

Chlorine  35,  37  Lead,  Bismuth— See  Fig.  2. 
Potassium  39,  41 


46  WITHIN  THE  ATOM 

has  been  made,  gives  the  observed  relation  between 
the  masses  of  the  atoms  of  various  chemical  elements 
as  determined  by  the  weights  of  equal  numbers  of 
atoms.  To  facilitate  the  expression  of  the  relations 
or  ratios  of  atomic  mass  the  ratios  are  all  referred  to 
oxygen  and  a  common  denominator  of  16  is  used  in 
their  expression.  The  various  numerators  of  the 
ratios  then  become  the  atomic  weights  of  the  various 
elements  in  terms  of  oxygen  as  16.  The  choice  of 
this  number  was  a  more  or  less  conscious  anticipation 
of  the  facts  of  today.  The  unit  of  weight  which  is 
used  in  the  expression  of  atomic  weights  is  the  weight 
of  one-sixteenth  of  the  oxygen  atom.  Today  we 
know  that  this  unit  is  the  weight,  or  more  strictly 
the  mass,  of  a  proton  which  is  associated  with  other 
protons  and  electrons  in  the  nuclear  structure  of  an 
atom.  To  a  close  approximation  this  unit  of  the 
table  of  atomic  weights  is  one-quarter  the  mass  of 
an  alpha  particle  and  hence  is  1845  tunes  the  unit 
of  mass  which  was  chosen  earlier  in  this  chapter. 

For  reasons  which  are  not  yet  evident  the  mass  of 
an  isolated  proton  is  not  exactly  one-sixteenth  of  the 
mass  of  an  oxygen  atom.  Relative  atomic  weights 
are  capable  of  sufficiently  exact  determination  so 
that  the  values  in  the  table  are  not  to  be  doubted. 
From  that  table  the  masses  of  the  atoms  of  hydrogen, 
helium  and  oxygen  are  respectively  1.0008,  4.00,  and 
16.00. 

Why  hydrogen  is  not  unity  is  not  known,  although 
plausible  explanations  may  be  given  in  terms  of 
electro-magnetic  theory.  When,  however,  we  con- 
sider that  mass  is  merely  a  factor  in  the  expression 


MASS  AND  INERTIA  OF  ATOMIC  SYSTEMS     47 

of  the  relationship  between  energy  and  speed,  it  be- 
comes conceivable  that  the  energy  relations  should 
be  slightly  different,  depending  upon  whether  or  not 
the  proton  is  nearly  or  entirely  isolated  or  is  inti- 
mately associated  with  other  protons  as  in  the  nuclei 
of  the  atoms  of  large  mass  and  large  atomic  number. 

Whenever  the  atomic  weight  of  a  chemical  ele- 
ment is  a  whole  number  within  the  limits  of  the  ex- 
perimental errors  involved  in  its  determination,  as, 
for  example,  in  the  cases  of  lithium,  nitrogen,  so- 
dium, and  sulphur,  we  have  reasons  to  expect  that 
the  substances  are  actually  chemical  elements  and 
not  mixtures  of  atomic  systems  with  equal  atomic 
numbers  but  unequal  nuclear  masses.  In  all  other 
cases  isotopes  are  suspected  and  recent  experiments 
have  shown  the  existence  of  the  proper  isotopes  to 
explain  the  failures  of  some  atomic  weights  to  be 
whole  numbers.  The  isotopes  so  far  discovered  are 
given  in  the  note  to  Table  V. 

One  of  the  most  interesting  illustrations  of  the  ex- 
istence of  isotopes  is  found  in  the  case  of  lead,  where 
a  large  number  are  known  to  exist.  Except  for  bis- 
muth all  the  elements  above  lead  in  atomic  number 
are  radioactive;  and  lead  seems  to  be  an  end-product 
of  several  different  series  of  radioactive  disintegra- 
tions which  we  shall  consider  in  the  next  chapter. 


CHAPTER  V 

RADIOACTIVE    DISINTEGRATIONS 

ATOMIC  systems  which  are  chemically  identical 
and  non-separable  occupy  the  same  place  in  the 
periodic  table  which  was  described  in  Chapter  III. 
The  basis  of  selection  for  position  is  the  atomic 
number.  Systems  with  the  same  atomic  number 
may,  however,  differ  in  atomic  mass,  in  previous 
history,  and  in  inner  tendencies  toward  radioactive 
displays.  When  the  atoms  of  such  isotopic  systems 
are  different  in  mass  they  may  be  separated  by 
physical  means,  but  those  of  isotopic  systems  which 
differ  in  inner  tendencies  cannot  be  separated. 
When,  however,  their  divergent  tendencies  actually 
result  in  different  radioactive  transformations  we 
may  reason  that  isotopes  do  exist. 

Radioactive  substances  have  been  described  as 
atomic  systems  which  are  dissatisfied  hi  their  nuclear 
structures.  In  an  individual  atom  such  dissatisfac- 
tion leads  to  a  nuclear  debacle,  after  which  the  atom 
is  generally  declassed.  Ultimately  all  the  individual 
atoms  of  a  radioactive  substance  will  undergo  the 
same  transformation.  By  some  inner  economy, 
however,  they  so  arrange  that  at  any  instant  a  defi- 
nite proportion  of  their  number  shall  be  engaged  in 
the  characteristic  activities  of  the  group,  that  is 

48 


RADIOACTIVE  DISINTEGRATIONS  49 

either  hurling  alpha  particles  or  shooting  forth  at 
high  speeds  the  lighter  beta  particles. 

When  an  atom  changes  in  its  nuclear  construction 
it  must  be  reclassified  and  assigned  to  another  place 
in  thp  periodic  table.  By  radioactive  changes  the 
atom  jumps  from  one  place  in  the  table  to  another. 
The  new  atomic  system,  which  embraces  the  atoms 
which  have  jumped,  differs  in  previous  history  and 
inner  tendencies  from  the  system  which  already  oc- 
cupies the  new  place  in  the  periodic  table.  With 
this  older  occupant  it  becomes  isotopic  but  mot 
identical. 

The  changes  in  position  in  the  periodic  table  which 
accompany  radioactivity  are  due  to  changes  in  the 
nuclear  structure  of  the  various  atomic  systems. 
The  nucleus  may  lose  an  alpha  particle  or  a  beta  par- 
ticle. A  loss  of  an  alpha  particle  reduces  the  number 
of  protons  in  the  nucleus  by  four  and  the  number  of 
electrons  by  two.  The  excess  of  protons  over  elec- 
trons, which  we  express  by  the  atomic  number,  is 
therefore  reduced  by  two.  Whenever  a  nucleus 
loses  an  alpha  particle  the  atom  is  declassed,  not  to 
the  class  immediately  below  but  to  that  two  below 
in  the  scale  of  atomic  numbers. 

When  an  atom  of  radium  loses  an  alpha  particle 
it  ceases  to  be  radium,  for  its  atomic  number  is  re- 
duced from  88  to  86.  This  new  substance  is  called 
niton,  or  "radium  emanation."  In  a  similar  manner 
when  an  atom  of  niton  loses  an  alpha  particle  it  be- 
comes isotopic  with  all  other  systems  of  atomic 
number  84. 

Before  discussing  this  series  of  changes  it  is  de- 


50  WITHIN  THE  ATOM 

sirable  to  consider  for  a  moment  what  happens  to  the 
alpha  particle  which  is  ejected.  It  is  the  nucleus  of 
a  helium  atom  and  needs  two  external  electrons  to 
become  a  satisfied,  inert  helium  atom.  In  the  first 
portion  of  its  mad  rush  outward  from  a  radioactive 
atom,  an  alpha  particle  seriously  disturbs  the  other 
atomic  systems  by  which  it  passes,  shaking  and 
knocking  loose  some  of  their  planetary  electrons. 
Its  effect  is  to  ionize  some  of  the  atoms  of  the  at- 
mosphere through  which  it  passes,  forming  atomic 
systems  which  are  unsatisfied  in  number  of  electrons, 
some  having  too  few  and  others,  which  have  ac- 
quired the  loosened  electrons  of  their  neighbors,  hav- 
ing too  majiy.  When  the  rush  of  the  alpha  particle 
has  been  stayed  it,  too,  becomes  as  the  other  atomic 
systems  of  the  atmosphere  and  finds  quantitative 
satisfaction  by  claiming  two  electrons  from  any 
system  which  has  more  than  it  needs  for  its  own 
satisfaction. 

The  subject  of  the  ionization  of  gases  by  alpha 
particles,  and  also  by  other  methods,  is  one  of  con- 
siderable interest  but  it  must  be  postponed.  For 
the  present  it  must  be  sufficient  to  say  that  in  the  at- 
mosphere of  the  earth  there  are  always  some  atomic 
systems  which  have  either  an  excess  or  a  deficiency 
of  electrons.  Whenever  in  the  wanderings  of  these 
systems  those  of  opposite  kinds  of  unsatisfaction 
meet  an  electron  is  transferred. 

The  fierce  rush  of  the  alpha  particle,  as  it  is  ejected 
from  the  nucleus  of  the  radioactive  atom,  is  capable 
of  dislocating  the  planetary  electrons  of  the  atom 
from  which  it  proceeds  just  as  well  as  those  of  other 


RADIOACTIVE  DISINTEGRATIONS  51 

atoms  which  it  meets  later.  Ite  departure  from  the 
nucleus  leaves  the  nucleus  a  net  excess  of  protons, 
two  less  than  before,  and  the  shells  of  planetary 
electrons  would  therefore  hold  an  excess  of  two 
electrons  if  the  alpha  particle  did  not  jar  them  loose 
into  outer  space.  It  is  not  content,  however,  with 
shaking  loose  enough  planetary  electrons  to  leave  the 
remaining  atomic  structure  neutral,  that  is  satisfied 
in  total  number  of  protons  and  electrons.  It  appears 
to  dislocate  several  electrons  and  so  to  leave  behind 
it  an  atomic  structure  reduced  by  two  in  atomic 
number  and  by  more  than  two  in  number  of  planet- 
ary electrons. 

The  effect  is  experimentally  observable  because  of 
the  phenomenon  of  recoil.  When  the  alpha  particle 
erupts,  it  kicks  back  the  structure  from  which  it  pro- 
ceeds. Because  of  the  larger  mass  of  the  system 
which  is  left  the  speed  of  its  recoil  is  much  less  than 
that  of  the  lighter  alpha  particle.  It  suffices,  how- 
ever, to  permit  a  segregation  of  the  two  products  of  a 
radioactive  disturbance. 

The  electrons,  which  the  departing  alpha  particle 
drags  from  its  own  original  atomic  surroundings, 
wander  about  as  free  electrons  or  are  acquired  by 
neighboring  atoms  which  thus  become  quantitatively 
unsatisfied.  From  them,  or  from  other  structures 
with  excess  electrons,  the  atomic  system,  which  re- 
sults from  the  emergence  of  an  alpha  particle,  may 
later  acquire  sufficient  electrons  to  be  quantitatively 
satisfied.  The  number  which  it  thus  adds  will  be 
such  as  to  make  the  number  of  planetary  electrons 
equal  to  the  new  atomic  number.  The  disintegra- 


52  WITHIN  THE  ATOM 

tion  product,  therefore,  of  an  emission  of  alpha  par- 
ticles is  a  substance  with  the  atomic  number  and  also 
the  configuration  of  planetary  electrons  which  cor- 
respond to  a  position  in  the  periodic  table  in  the 
second  place  below  that  occupied  by  the  atomic 
system  of  the  original  substance.  The  atomic  mass 
of  the  disintegration  product  is,  of  course,  four  units 
less  than  that  of  the  original  atom,  because  each 
alpha  particle  removes  four  protons. 

An  opposite  type  of  change  occurs  when  a  beta 
particle  is  ejected  from  the  nucleus  of  a  radioactive 
atom.  The  atomic  number  is  increased  by  one,  since 
the  excess  of  protons  in  the  nucleus  is  increased  by 
the  subtraction  of  an  electron.  In  the  planetary 
system  of  the  atom  there  is  then  an  excess  of  one 
electron  over  the  number  necessary  for  quantitative 
satisfaction  of  the  system.  The  extra  electron  is 
loosely  held  and  therefore  it  is  shortly  acquired  by 
some  atom  which  wanders  into  the  neighborhood. 
The  net  result  i§  an  increase  of  one  in  the  atomic 
number  and  a  configuration  of  planetary  electrons 
which  corresponds  to  the  new  atomic  number.  The 
disintegration  product  of  a  radioactive  change 
which  is  accompanied  by  the  expulsion  of  an  electron 
is  therefore  isotopic  with  the  atomic  system  of 
number  next  higher  than  the  original  system.  The 
expulsion  of  an  electron,  however,  is  unaccompanied 
by  any  appreciable  change  in  mass,  for  we  consider 
the  mass  of  an  atom  to  be  due  essentially  to  the  pro- 
tons which  enter  into  its  nuclear  construction. 

A  glance  at  the  diagrammatic  representation  of 
the  periodic  table  which  is  given  on  page  33  shows 


RADIOACTIVE  DISINTEGRATIONS  53 

that  the  atom  moves  two  places  (clockwise)  if  there 
is  expelled  an  alpha  particle  and  one  place  (counter- 
clockwise) if  a  beta  particle  is  expelled.  Two  suc- 
cessive expulsions  of  beta  particles  will  therefore 
neutralize  the  effect  of  one  expulsion  of  an  alpha  par- 
ticle so  far  as  concerns  position  in  the  table.  It  will 
not  neutralize  the  change  in  mass,  however,  for  the 
"beta  ray"  change,  as  it  is  called,  is  without  effect  on 
atomic  mass,  while  the  "alpha  ray"  change  produces 
a  reduction  of  four  units  in  atomic  mass. 

It  therefore  happens  that  a  radioactive  substance 
may  undergo  such  a  succession  of  changes  as  to  pro- 
duce a  substance  isotopic  with  the  original  substance, 
chemically  indistinguishable,  but  four  units  less  in 
atomic  weight.  This  is  true,  for  example,  in  the  case 
of  uranium  which  ejects  an  alpha  particle,  forming 
Uranium  XT,  as  it  is  called.  This  substance  ejects 
a  beta  particle,  forming  Uranium  Xn,  and  the  latter 
ejects  another  beta  particle,  forming  Uranium  II, 
so-called,  which  is  isotopic  with  uranium. 

Altogether  some  thirty-eight  radioactive  sub- 
stances have  been  discovered.  All  these,  however, 
find  their  places  in  the  periodic  table  between  urani- 
um, with  an  atomic  number  of  92,  and  lead,  with  a 
number  of  82.  All  are  products  of  the  disintegra- 
tion of  two  elementary  substances,  uranium  and 
thorium.  Radium,  the  most  famous,  is  a  product 
in  the  disintegration  series  of  uranium.  In  terms  of 
these  elements,  uranium  and  thorium,  modern 
science  accounts  for  all  the  known  radioactive 
products. 

The  inner  structure  and  history  of  the  atoms  of 


WITHIN  THE  ATOM 


any  radioactive  substance  are  not  the  same  for  all. 
There  are  points  in  the  series  of  uranium,  for  ex- 
ample, where  two  distinct  disintegration  products 
may  be  formed.  The  entire  series  with  its  several 
branches  is  shown  diagrammatically  in  Fig.  2. 
Changes  produced  by  alpha  rays  are  indicated  by 
heavy  arrows,  and  those  of  beta  rays  by  lighter  ar- 


URANIUM        U.n 
S\ 


ff.Xs    |^V    Protoactinium 
.Xf        /JLiSKK    \     Kadwct. 
ActiniumX 


Radium 


\ 


Ra.  Emanation 


THORIUM  Radiofh 

s 


Mesoth;      Th 


Th.Em. 


Polonium 


C'     Ra.A 


Ac-c 


1 


Ra.C2 


Th.C2 


Ac.D 


Th.B 


Th.D 


FIG.  2 

Radioactive  Transformations.  Atomic  numbers  are  given  by 
the  vertical  scale.  Alpha  ray  changes  are  indicated  by  heavy 
arrows.  These  decrease  atomic  number  by  two,  and  atomic  weight 
by  four.  Beta  ray  changes  are  indicated  by  light  arrows.  These 
increase  atomic  number  by  one,  but  do  not  affect  atomic  weight. 

rows.  All  the  substances  in  the  same  horizontal  line 
have  the  same  atomic  number  but  may  have  differ- 
ent masses. 

From  this  diagram  it  appears  that  there  is  a  rel- 
atively large  number  of  isotopes  of  lead,  for  the  end- 
products  of  the  various  series  fall  in  the  place  at  the 
periodic  table  which  is  occupied  by  lead  with  its 


RADIOACTIVE  DISINTEGRATIONS  55 

atomic  number  of  82.  Under  ordinary  conditions 
what  we  know  as  lead  is  a  mixture  of  several  of  these 
isotopes  and  has  an  atomic  mass  which  depends  upon 
the  atomic  masses  and  proportions  of  its  constitu- 
ents. 

Several  experimental  studies  have  been  made  of 
lead  derived  from  different  mineral  deposits  to  de- 
termine whether  or  not  such  differences  in  atomic 
weight  actually  existed  and  conformed  to  the  prob- 
able radioactive  antecedents.  For  example,  an  ex- 
amination of  the  lead  derived  from  Ceylon  thorite 
gave  207.69  as  compared  to  207.2  which  is  the  ordi- 
nary value.  This  mineral  contains  55  per  cent  of 
thorium,  1  to  2  per  cent  of  uranium,  and  about  0.4 
per  cent  of  lead,  an  amount  so  small  as  to  be  un- 
doubtedly of  radioactive  origin.  The  lead  in  this 
mineral  should  be  largely  due  to  thorium  unless  the 
rate  of  disintegration  of  uranium  is  many  tunes 
greater  than  that  of  thorium.  Since  it  is  only  two  or 
three  tunes  greater,  the  lead  in  this  ore  should  be 
about  ten  parts  of  thorium  origin  for  each  part  of 
uranium  origin.  Other  similar  experiments  have 
been  performed  on  samples  of  lead  with  different 
radioactive  antecedents,  and  atomic  weights  have 
been  obtained  which  range  from  206.1  to  207.7. 

Such  experiments  are  but  a  small  part  of  the  care- 
ful, ingenious,  and  thorough  study  *  of  radioactive 
substances  which  has  been  responsible  for  the 
modern  theory  of  isotopes.  This  theory  has  been 
corroborated  by  the  discovery  of  isotopes  among  the 

*To  this  study  the  chief  contributions  have  been  made  by 
Soddy  and  Rutherford.  To  the  former  is  due  the  concept  of 
isotopes. 


56  WITHIN  THE  ATOM 

atomic  systems  of  lower  atomic  number.  Some  re- 
sults of  such  investigation  were  mentioned  in  the 
preceding  chapter.  The  most  potent  method  is  that 
involving  so-called  "positive  rays"  but  purely  me- 
chanical methods  such  as  diffusion  have  been  used 
to  produce  a  separation  of  isotopes. 

Within  the  last  twenty  years  the  whole  basis  for 
our  conception  of  matter  has  changed.  Today  we 
know  no  matter  but  only  electricity.  Our  atoms 
are  no  longer  "uncut"  but  are  complex  structures  of 
protons  and  electrons.  Their  masses  are  due  to  the 
protons  and  their  chemical  behaviour  to  the  plane- 
tary electrons  which  encircle  the  nucleus.  From  the 
standpoint  of  chemical  behaviour  there  are  only 
ninety-two  possible  types  of  systems  and  these  are 
distinguished  by  the  excess  of  protons  in  their  nuclei. 
Some  of  these  types  include  structures  of  radically 
different  atomic  mass,  history,  and  stability  of  nu- 
cleus. Those  of  unstable  nuclear  construction  change 
from  type  to  type  in  conformity  with  a  definite  law, 
shifting  their  positions  at  the  periodic  table  of  ele- 
mental types. 

Such  is  the  matter  with  which  the  new  science 
deals.  All  phenomena  of  matter,  such  as  cohesion, 
vaporization,  capillarity,  elasticity,  heat  conductivi- 
ty, light  and  heat  radiation  or  photochemical  effects, 
must  finally  be  explained  in  terms  of  a  matter  which 
is  granular  in  structure  and  electrical  in  character. 
Unfortunately  there  remain  today  wide  gaps  in  our 
knowledge.  The  first  step,  however,  toward  an  ap- 
preciation of  what  is  known  is  the  consideration  of 
those  phenomena  usually  classified  under  the  term 
"'electricity." 


CHAPTER  VI 

CONDUCTION   OF   ELECTRICITY  THROUGH   GASES 

IN  the  preceding  chapters  the  discussion  of  atomic 
systems  has  been  limited  almost  entirely  to  those 
systems  which  are  quantitatively  satisfied,  so-called 
normal  or  uncharged  atoms.  The  abilities  of 
various  atoms  to  enter  into  molecular  unions  with 
other  atoms  has  been  attributed  to  the  unsatisfactory 
configurations  of  their  planetary  electrons.  In  the 
formation  of  such  unions  configurations  are  attained' 
which  represent  net  increases  in  satisfaction  or 
stability.  The  molecules  so  formed  are,  of  course, 
satisfied  also  in  equivalence  of  electrons  and  protons 
and  are  normal  molecular  systems.  Under  certain 
conditions,  of  which  Chapter  II  contained  an  illus- 
tration in  the  dissociation  of  sodium  chloride,  a 
molecular  system  may  split  into  two  parts  each  of 
which  preserves  some  satisfaction  of  configuration  at 
the  expense  of  a  satisfaction  in  quantity.  The 
separate  parts  are  called  ions;  and  one  has  an  excess 
of  protons  while  the  other  has  an  excess  of  electrons. 

Whenever  any  body  has  an  excess  of  protons, 
whether  the  body  be  of  atomic  size  or  as  big  as  the 
earth,  we  shall  say  that  it  is  "positively  charged" 
with  electricity;  and  similarly  we  shall  call  a  body 
with  an  excess  of  electrons  "negatively  charged." 

57 


58  WITHIN  THE  ATOM 

Of  the  various  possible  ways  of  charging  a  body  with 
electricity  we  shall  consider  first  the  so-called  fric- 
tional  method  which  originally  excited  attention  to 
the  peculiar  properties  of  amber. 

Suppose  two  dissimilar  substances  are  brought  into 
close  relations  by  rubbing.  In  general  there  will  be 
an  appreciable  difference  between  the  substances  in 
the  matter  of  what  constitutes  a  satisfactory  con- 
figuration for  the  electrons  of  their  molecules,  for 
one  may  have  a  greater  need  for  electrons  than  the 
other.  Although  the  surfaces  may  appear  smooth 
the  structure  of  their  atoms  is  such  that  the  act  of 
rubbing  two  bodies  together  is  really  the  act  of 
crowding  one  planetary  system  into  another  or  caus- 
ing one  to  pass  through  the  other.  There  is  every 
opportunity  for  some  of  the  electrons  to  be  displaced 
from  their  own  planetary  systems  and  to  join  those 
of  other  nuclei.  The  molecules  of  the  system  which 
has  the  greater  need  for  electrons  will  gain  or  that 
which  would  more  willingly  assume  a  configuration 
with  fewer  electrons  will  lose.  The  net  result  when 
the  substances  are  separated  is  that  one  has  more 
than  its  normal  number  and  the  other  less;  the  first 
is  negative  and  the  second  positive  in  charge. 

The  classical  substances  are  glass  and  silk,  or  cat's 
fur  and  sealing  wax.  The  first  of  each  pair  acquires 
a  positive  charge  and  the  second  a  negative  charge. 

The  act  of  separating  the  substances  is  done 
against  the  attraction  of  the  excess  protons  of  one 
body  for  the  excess  electrons  which  are  being  left  be- 
hind on  the  other  body.  The  act  requires  work  for 
the  charged  bodies  tractate.  If  free  to  move  into 


CONDUCTION  OF  ELECTRICITY  59 

contact  they  will  do  so,  and  the  electrons  which  were 
foisted  upon  the  unsuspecting  electronegative 
systems  of  one  body  will  return  to  the  electroposi- 
tive systems  of  the  other,  restoring  the  quantitative 
equilibrium. 

In  their  motion  of  returning  to  each  other  the 
charged  bodies  manifest  energy.  This  energy  is  con- 
tributed during  the  act  of  separation,  is  potential 
while  they  are  held  apart,  and  is  converted  into 
kinetic  energy  as  they  move  toward  each  other.  At 
the  moment  of  impact  the  kinetic  energy  of  the 
electrified  bodies  is  passed  on  to  their  invisible  mole- 
cules, atoms,  and  electrical  elements,  contributing  to 
them  haphazard  motions  which  we  recognize  as 
heat.  Of  such  conversions  or  transferences  of 
energy,  however,  more  will  need  to  be  said  later. 

Because  two  oppositely  electrified  bodies  will  so 
move  toward  each  other  and  thus  manifest  energy 
we  say  that  they  possess  when  held  apart  a  potential 
energy.  Since  we  believe  that  energy  is  indestructi- 
ble we  measure  this  potential  energy  either  by  the 
energy  originally  required  to  produce  the  separation 
or  by  that  which  may  be  derived  from  a  return  of 
the  electrical  elements  to  the  normal  condition  of 
equal  numbers  of  protons  and  electrons. 

The  return,  however,  need  not  be  accomplished  by 
the  actual  motion  of  the  two  oppositely  charged 
bodies,  which  may  indeed  possess  billions  of  normal 
atoms  for  every  one  which  is  charged.  Any  method 
which  will  transfer  electrons  from  the  negative  body 
to  the  positive  will  bring  about  the  original  stable 
condition.  To  all  methods  we  give  the  general  name 


60  WITHIN  THE  ATOM 

of  "electrical  conduction"  and  to  the  medium 
through  which  conduction  takes  place  we  ascribe  a 
characteristic  of  electrical  conductivity.  With  some 
of  the  methods  of  obtaining  conductivity  and  with 
the  corresponding  mechanisms  for  conduction  the  re- 
mainder of  this  chapter  will  deal. 

Whether  by  some  adaptation  of  the  crude  method 
of  electrification  by  friction,  or  by  such  more  efficient 
means  as  dynamo-electrical  machinery  offers,  we 
may  give  opposite  electrical  charges  to  two  bodies. 
Such  a  condition  is  conveniently  evaluated  as  a 
magnitude,  known  as  electrical  potential,  which 
represents  the  potential  energy  of  the  last  electron 
to  be  added  to  the  negative  body,  and  hence  the 
energy  which  is  released  by  the  return  of  this  elec- 
tron to  its  former  home.  There  is  something  of  the 
idea  of  marginal  utility  in  this  concept  of  electrical 
potential  for  we  always  measure  it  by  the  energy 
corresponding  to  the  last  electron  to  be  added.  The 
comparison,  however,  is  without  stigma. 

Whatever  path  this  marginal  electron  may  travel 
in  a  return  trip  the  total  amount  of  energy  thereby 
converted  from  potential  into  kinetic  is  always  the 
same  and  its  value  is  the  electrical  potential  between 
the  two  charged  bodies.  The  movement  of  an 
electron  from  a  negative  to  a  positive  body  is  a 
descent  from  a  height,  from  a  place  of  high  potential 
energy  to  a  place  of  zero  possibilities  in  energy.  As 
it  falls  it  acquires  kinetic  energy  and  the  potentiali- 
ties are  decreased.  In  steep  places  the  conversion  is 
rapid,  not  necessarily  with  respect  to  time,  but  rather 
with  respect  to  space.  Just  as  we  measure  the 


CONDUCTION  OF  ELECTRICITY  61 

grades  of  roads  in  feet  of  descent  per  mile  of  length, 
so  we  measure  the  "potential  gradient"  by  the  de- 
crease in  potential  for  each  centimeter.  In  all  the 
phenomena  of  conduction  of  electricity  the  impor- 
tant magnitude  is  this  potential  gradient,  for  it  is 
the  space  rate  at  which  a  body,  carrying  an  excess 
proton  or  an  excess  electron,  will  acquire  kinetic 
energy. 

If  conduction  occurs  between  two  oppositely 
charged  plates  it  may  take  place,  depending  upon  the 
conditions,  in  any  one  or  any  combination  of  three 
distinct  manners.  There  may  be  a  motion  of  elec- 
trons from  the  negative  plate  to  the  positive,  a  mo- 
tion of  protons  in  the  opposite  direction,  or  a 
friendly  service  on  the  part  of  molecular  or  atomic 
systems  which  lie  between  the  two  plates.  The  last 
case  is  that  of  conduction  through  gases  and  also 
through  conducting  liquids  such  as  the  salt  solution 
to  which  reference  was  made  earlier  in  this  chapter. 

Ordinarily  an  atom  or  a  molecule  of  a  gas  is  in- 
capable of  assisting  in  electrical  conduction.  To 
serve,  it  must  be  ionized,  that  is  be  split  into  two 
parts  which  are  quantitatively  unsatisfied,  one  part 
positive  and  the  other  negative. 

In  any  gas  the  various  molecules  are  always  in 
more  or  less  violent  haphazard  motion.  The  greater 
the  temperature  the  higher  the  speed  with  which 
they  are  moving,  for  temperature  is  merely  our  con- 
ventional term  for  expressing  the  degree  of  thermal 
agitation  of  the  molecules  of  a  substance.  Each 
molecule  travels  in  a  straight  line  until  its  approach 
to  another  molecule  causes  it  to  swerve.  There  is  no 


62  WITHIN  THE  ATOM 

real  collision  but  rather  a  respect  for  each  other's 
sphere  of  influence  which  results  in  a  mutual  change 
of  direction  when  these  spheres  are  in  danger  of  col- 
lision. On  the  average  between  successive  adapta- 
tions to  the  presence  of  its  neighbors  a  molecule 
travels  a  distance  relatively  large  as  compared  to  its 
own  size. 

Now  let  us  suppose  that  hi  the  space  between  these 
widely  separated  molecules  there  are  some  free  elec- 
trons, that  is  electrons  which  have  been  dislodged 
from  their  original  atomic  systems.  These  also 
wander  about,  choosing  the  easiest  way  and  usually 
avoiding  difficulties  although  an  individual  electron 
may  now  and  then  strike  into  the  planetary  system 
of  a  molecule  and  become  attached  to  it.1  If  it  does 
we  have  a  negatively  charged  molecule;  if  it  does  not 
we  have  a  free  electron.  In  either  case  we  have  a 
very  different  phenomenon  as  soon  as  this  gas  is 
placed  between  two  plates  which  are  oppositely 
charged.  Then  there  is  added  to  the  haphazard 
motion  of  the  free  electrons,  or  of  those  molecules 
which  have  acquired  a  negative  charge  by  adding  an 
electron,  a  directed  motion  due  to  the  charged  plates. 
Only  those  molecular  systems  which  are  uncharged 
are  uninfluenced. 

Each  of  the  charged  molecules  or  ions,  as  they 
should  be  called,  now  finds  itself  at  some  point  or 
other  along  a  path  between  the  plates  and  starts  to 
fall  from  this  point  toward  the  positively  charged 

1  Whether  or  not  the  atoms  or  molecules  of  the  atmosphere 
acquire  these  wandering  electrons  depends  upon  their  type.  Inert 
gases  certainly  can  not;  gases  like  oxygen,  however,  can  because 
their  atoms  have  external  shells  incompletely  filled  by  electrons. 


CONDUCTION  OF  ELECTRICITY  63 

plate.  If  the  potential  gradient  is  small  the  result 
is  merely  a  drift  of  the  negative  ions  and  electrons 
toward  this  plate  as  a  goal.  A  possible  comparison 
is  the  guided  drift  of  a  herd  of  cattle  which  a  rancher 
is  leisurely  driving  across  the  plains. 

The  larger  the  potential  gradient  at  any  point, 
that  is  the  more  rapidly  a  negative  ion  or  an  electron 
falls  toward  the  positive  plate,  the  greater  is  the 
possibility  of  its  plunging  into  the  atomic  system  of 
some  molecule,  which  may  be  in  its  path,  and  gen- 
erally dislocating  this  system.  If  it  falls  far  enough 
to  acquire  a  certain  definite  amount  of  energy  it  will 
knock1  an  electron  loose  from  the  molecule  with 
which  it  collides,  and  then  continue  on  its  own  way 
toward  its  positive  goal.  As  soon  as  it  has  again 
fallen  far  enough  to  acquire  the  necessary  energy  it 
is  ready  to  ionize  another  molecular  system. 

Each  time  it  does  so  it  leaves  behind  a  free  electron 
and  a  positive  ion,  that  is  a  molecular  system  which 
has  lost  an  electron  and  so  has  an  excess  of  protons. 
These  also  take  up  directed  motions,  the  electron 
moving  toward  the  positive  plate  and  the  positive 
ion  moving  in  the  opposite  direction.  Both  of  these 
newly  formed  systems  are  able  to  ionize  uncharged 
molecules  with  which  they  collide  provided  that  be- 
tween successive  collisions  they  fall  sufficiently  far 
to  acquire  the  necessary  amount  of  energy. 

The  process  is  obviously  cumulative;  and  what 
starts  as  a  drift  of  the  occasional  unemployed  elec- 
tron becomes  a  stream  of  oppositely  directed  and  op- 

1  The  word  "knock"  is  convenient  although  "crowd"  is  more 
exact  for  there  is  no  actual  contact  in  a  "collision." 


64  WITHIN  THE  ATOM 

positely  charged  particles,  both  ions  and  electrons. 
A  current  of  electricity  is  now  said  to  be  flowing  be- 
tween the  two  plates.  The  net  effect  of  the  motions 
of  these  ions  and  electrons  is  to  carry  protons  to  the 
negatively  charged  plate  and  electrons  to  the  posi- 
tively charged  plate.  When  a  positive  gaseous  ion 
reaches  the  negative  plate  it  acquires  from  it  an 
electron  which  satisfies  its  own  requirement  and  re- 
duces the  unsatisfaction  of  the  negative  plate.  Simi- 
larly the  electrons  which  arrive  at  the  positive  plate 
join  its  atomic  systems  and  reduce  their  unsatisfac- 
tion. 

In  describing  this  general  phenomenon  of  the  con- 
duction of  electricity  through  gases  we  have  as- 
sumed, first,  the  presence  in  the  gas  of  some  free 
electrons  or  negative  ions,  and  second,  a  potential 
gradient  between  successive  collisions  such  that  these 
ions  acquire  sufficient  energy  to  ionize  the  gas  mole- 
cules with  which  they  collide. 

The  first  condition  is  always  met  by  the  atmos- 
pheric gases  above  the  earth,  for  it  so  happens  there 
is  a  sufficiency  of  radioactive  transformations  l  al- 
ways going  on  within  the- earth  to  provide  a  fair 
number  of  electrons  in  each  portion  of  the  atmos- 
phere. These  electrons  are  wrenched  from  their 
original  atomic  systems  by  the  so-called  gamma  rays 
which  usually  accompany  the  beta  rays.  While  the 
beta  rays  are  not  rays  at  all  but  are  expelled  electrons 
the  gamma  rays  are  strictly  a  radiation  of  energy 

1  Electrons  are  also  freed  in  large  numbers  by  the  ultra-violet 
rays  from  the  sun.  This  is  a  more  important  source.  The 
phenomenon  is  mentioned  later  and  also  considered  in  detail  in 
Chapter  XI. 


CONDUCTION  OF  ELECTRICITY  65 

similar  to  light  radiation,  but  most  closely  allied  to 
X-rays.  Ordinary  matter  is  not  very  opaque  to 
these  radiations,  which  are  extremely  penetrating 
and  thus  ionize  gases  far  from  their  source.  The 
second  condition  is  usually  within  the  control  of  the 
experimenter,  for  electrical  potentials  of  a  wide  range 
of  values  are  possible  by  the  use  of  electric  batteries 
or  dynamos. 

The  amount  of  energy  which  must  be  acquired  by 
an  electron  or  ion  in  order,  by  its  impact,  to  ionize 
a  normal  molecule  or  atom  is  dependent  upon  the 
character  of  the  latter.  It  is  obvious,  for  example, 
that  the  ionizing  potential  which  is  required  for  the 
disruption  of  an  atom  of  helium,  or  of  any  other  inert 
gas,  into  a  free  electron  and  an  atomic  system  which 
is  positive  by  virtue  of  a  lost  electron,  will  be  greater 
than  that  required  for  the  ionization  of  some  electro- 
positive element,  like  sodium,  where  the  system 
contains  one  electron  more  than  its  most  stable  con- 
figuration would  require.  The  ionizing  potential  de- 
pends upon  the  electronic  configuration  of  the  atom 
or  molecule  in  much  the  same  way  as  does  the 
chemical  valence. 

There  are  many  interesting  phenomena  connected 
with  the  conduction  of  electricity  through  gases 
which  merit  and  will  receive  later  some  discussion. 
For  example,  the  oppositely  directed  streams  of  posi- 
tive and  negative  ions  may  have  collisions  among 
themselves  which  result  in  the  formation  of  un- 
charged molecules.  On  the  other  hand,  the  impacts 
of  collision  may  be  insufficient  to  cause  ionization 
and  yet  be  sufficient  to  cause  such  a  readjustment 


66  WITHIN  THE  ATOM 

of  the  electronic  constituents  of  the  atom  as  to  result 
in  a  radiation  from  it  of  light  with  a  characteristic 
color.  The  characteristic  radiation  which  is  emitted 
by  the  molecules  of  the  gas  is  not  entirely  visible  to 
the  human  eye  for  some  of  it  lies  beyond  the  violet. 
These  ultra-violet  radiations  are  capable  of  shaking 
loose  electrons  of  substances  upon  which  they  im- 
pinge. When,  therefore,  they  strike  the  negative 
plate  and  so  shake  loose  electrons  from  some  of  its 
atoms,  the  freed  electrons  are  repelled  from  the  plate 
into  the  surrounding  gas  where  they  take  paths  to- 
ward the  positive  plate. 

At  the  negative  plate  electrons  may  be  freed  if  the 
impacts  of  the  positive  ions  are  sufficient  to  disrupt 
the  atomic  systems  of  which  the  plate  is  composed. 
The  bombardment  of  the  plate  results  also  in  a  gen- 
eral thermal  agitation  of  its  constituents  which  is 
manifested  by  a  rise  in  temperature. 

Before  discussing  some  of  these  phenomena  in 
more  detail  a  few  words  should  be  devoted  to  that 
type  of  conduction  which  occurs  when  molecular 
systems  dissociate  in  solution.  The  example  which 
was  given  earlier  is  that  of  sodium  chloride.  Quite 
a  large  group  of  chemical  compounds  will  dissociate 
in  this  manner  and  these  are  known  as  ionogens  or 
electrolytes.  They  may  be  divided  further  into  three 
classes.  The  first  of  these,  known  as  acids,  give  as 
one  product  of  the  dissociation  positively  charged 
ions  which  are  nothing  more  or  less  than  protons,  al- 
though they  are  commonly  known  as  hydrogen  ions. 
They  are  hydrogen  atoms  which  have  each  lost  an 
electron  to  their  previous  partners  in  molecular 


CONDUCTION  OF  ELECTRICITY  67 

union.  An  example  would  be  hydrochloric  acid, 
HC1.  The  second  type  yields  negative  ions,  Oil, 
which  are  composed  of  one  oxygen  and  one  hydro- 
gen atom  in  a  molecular  union,  but  have  retained 
one  electron  from  their  former  associates.  Such 
compounds  are  called  bases.  An  example  is  sodium 
hydroxide,  that  is,  caustic  soda,  which  is  symbolised 
as  NaOH.  The  third  type,  known  as  salts,  is  the 
result  of  mixing  solutions  of  an  acid  and  a  base. 
Under+  these  conditions  the  positive  and  negative 
ions,  H  and  OH,  combine,  as  often  as  they  meet,  to 
form  H20  and  the  other  ions  when  they  meet  form 
molecules  of  a  salt  which  may  or  may  not  be  soluble. 
Of  this  type  NaCl  is  an  example. 

The  dissociation  is  not  the  result  of  collisions  or 
of  ionization  hi  any  way  similar  to  that  discussed 
above  for  gaseous  molecules.  It  is  in  the  nature  of  a 
spontaneous  parting  of  the  molecular  system  because 
of  the  attracting  influences  of  the  neighboring  mole- 
cules of  water.  The  ions  then  pursue  haphazard 
paths  in  the  same  way  as  do  all  the  molecular 
systems  which  compose  the  liquid.  If  oppositely 
charged  plates  are  immersed  in  the  electrolyte,  the 
ions  are  given  directed  motions  in  addition  to  their 
own  natural  haphazard  motions.  The  positive  ions 
proceed  to  the  negative  plate  and  the  negative  ions  to 
the  other  plate.  When  they  make  contact  with 
these  plates  their  quantitative  unsatisfactions  are 
appeased  and  they  become  uncharged  atomic  or 
molecular  structures.  In  this  form  they  are  either 
deposited  on  the  plates  or  liberated  as  bubbles  of 
gas. 


68  WITHIN  THE  ATOM 

With  certain  electrolytes  there  may  occur  second- 
ary chemical  reactions  so  that  the  substance  which  is 
liberated  at  the  plate  is  not  that  which  traveled 
through  the  solution  as  an  ion.  For  example,  when 
the  electrolyte  is  dilute  sulphuric  acid,  that  is  H2S04 
and  H20,  the  two  hydrogen  ions,  each  H,  travel  to 
the  negative  plate  and  there  are_liberated  as  hydro- 
gen gas.  The  sulphate  radical,  SO4  after  delivering 
two  electrons  to  the  positive  plate,  combines  with  a 
water  molecule  to  form  more  sulphuric  acid.  The 
oxygen  atom  thus  released  then  joins  with  another 
atom  of  similar  experience  to  form  a  molecule  which 
appears  as  oxygen  gas,  O2.  By  means,  therefore,  of 
the  electric  current  and  the  secondary  chemical 
action,  water  is  decomposed  into  its  chemical  con- 
stituents. 


CHAPTER  VII 

CONDUCTION  THROUGH  SOLIDS  AND  OTHER 
ELECTRICAL  PHENOMENA 

IN  solid  bodies  the  molecules  or  atoms  are  re- 
stricted in  their  motions  and  do  not  wander  from 
one  part  to  another  as  do  the  molecules  of  liquids 
and  gases.  Through  solids,  therefore,  the  conduc- 
tion of  electricity  can  occur  only  as  the  result  of  the 
motion  of  electrons.  The  solid  substances  which 
conduct  electricity  best  are  metals,  the  elements 
whose  atoms  are  most  prone  to  part  with  an  electron. 
These  require  the  smallest  potential  relative  to  the 
ensuing  stream  of  electrons. 

The  atoms  of  metals  apparently  do  not  form  poly- 
atomic molecules,  so  that  in  conduction  through 
metallic  solids  we  have  to  do  only  with  atoms.  The 
close  grouping  of  atoms  in  solids  is  probably  re- 
sponsible for  a  certain  freedom  on  the  part  of  their 
electrons  since  it  may  mean  that  some  of  the  planet- 
ary electrons  of  one  atom  are  at  times  within  the 
sphere  of  influence  of  another  atom.  In  that  case 
they  might  serve  a  dual  purpose  of  partially  satis- 
fying the  claim  of  their  own  nuclei  and  that  of  the 
adjacent  atom.  By  such  double  service  they  would 
release  other  electrons  of  their  respective  atoms  for 
more  or  less  free  wandering  throughout  the  sub- 


70  WITHIN  THE  ATOM 

stance.  The  latter  electrons  would  be  akin  in  free- 
dom to  the  molecules  of  a  liquid  and  would  be 
restrained  from  excursions  beyond  the  solid  by  the 
attractions  of  the  nuclei  of  the  surface  atoms.  Under 
certain  conditions,  as  we  shall  see  on  page  73,  some 
may  pass  beyond  the  surface  and  appear  in  space  as 
free  electrons. 

We  might  form  a  picture  of  a  solid  conductor  of 
electricity  by  imagining  an  enormous  basket  ball 
court  on  which  there  are  disposed  a  large  number 
of  players.  Each  is  assigned  to  a  relatively  small 
circular  space  within  which  he  is  free  to  move.  The 
space  may,  however,  overlap  somewhat  those  as- 
signed to  his  neighbors  so  that  even  within  his  own 
circle  a  player's  movements  are  sometimes  restricted 
by  the  necessity  of  avoiding  a  collision  with  a  neigh- 
bor. A  large  number  of  basket  balls  are  being  tossed 
rapidly  about  from  player  to  player.  The  latter 
correspond  to  the  atoms  and  the  balls  to  the  wander- 
ing electrons.  There  is  always  activity  but  the  balls 
only  fly  wild,  beyond  the  boundaries  of  the  court, 
when  there  is  a  very  considerable  (thermal)  agita- 
tion, as  will  be  explained  later. 

Now  suppose  that  each  second  we  throw  into  the 
court  at  one  end  a  large  number  of  balls  and  with- 
draw an  equal  number  from  the  opposite  end.  We 
do  not  alter  the  number  within  the  court  at  any  in- 
stant, but  we  do  require  that  the  haphazard  motion 
shall  be  largely  superseded  by  a  directed  motion. 
This  in  effect  is  what  happens  when  there  is  a  po- 
tential between  the  two  ends  of  a  solid  'conductor. 


CONDUCTION  THROUGH  SOLIDS'  71 

Each  atom-player  must  pass  to  one  of  his  neighbors 
who  is  nearer  the  positive  goal. 

Usually  this  is  most  effectively  accomplished  if 
the  players  are  not  dashing  about  too  rapidly  and 
moving  too  far.  On  the  other  hand,  as  the  thermal 
agitation  increases  there  seems  to  be  more  difficulty 
in  securing  the  passage  of  the  same  current,  that  is 
the  same  number  of  electrons  a  second.  A  higher 
potential  is  required  or  there  is  a  lower  current  for 
the  same  potential.  Under  these  conditions  we  say 
that  the  conductor  has  a  higher  electrical  resistance. 
For  most  substances  the  resistance  increases  as  the 
temperature  rises. 

Conversely,  as  the  temperature  is  lowered  the  re- 
sistance decreases.  The  decrease  is  a  definite  frac- 
tional amount  for  each  degree  of  temperature,  and 
indicates  an  extremely  low  temperature,  at  which  we 
should  expect  no  resistance  but  instead  perfect  con- 
ductivity. This  temperature,  which  is  the  absolute 
zero  and  is  discussed  on  page  173,  has  never  been  at- 
tained, although  closely  approached.  It  represents 
a  condition  in  which  there  is  no  thermal  agitation  of 
the  atoms  of  the  substance.  Under  these  conditions 
the  atoms  would  be  closely  packed  together  and  an 
electron  could  be  passed  from  one  to  the  other  with- 
out requiring  that  it  should  ever  pass  beyond  the 
influence  of  an  atomic  nucleus. 

Under  ordinary  conditions  it  is  believed  that  an 
electron  shoots  clear  of  its  original  atom  and  pro- 
ceeds across  free  space  until  it  comes  into  the  sphere 
of  another  atom,  just  like  the  basket  ball  of  our 
illustration.  To  free  an  electron  from  an  atomic 


72  WITHIN  THE  ATOM 

structure  requires  an  expenditure  of  energy  and  ac- 
cording to  the  most  recent  theory,  that  of  Bridgman, 
the  solid  offers  resistance  because  the  electron  must 
travel  gaps  between  atomic  systems.  Within  the 
sphere  of  influence  of  an  atom  the  electron  is  be- 
lieved to  move  freely.  Upon  this  basis,  and  sup- 
ported by  many  experiments,  Bridgman  is  develop- 
ing an  apparently  satisfactory  theory  of  metallic 
conduction.  According  to  this  theory,  when  the 
atoms  no  longer  dash  to  and  fro  they  may  be  so  close 
that  an  electron  passes  from  one  to  the  next  essen- 
tially without  crossing  any  gap. 

Some  substances,  however,  usually  relatively  poor 
conductors,  decrease  in  electrical  resistance  as  their 
temperature  is  increased.  In  such  a  case  it  is  prob- 
able that  the  electrons  are  not  so  easily  shot  from 
one  player  to  the  next  and  a  sort  of  hand-to-hand 
transfer  is  required.  If  the  player-atoms  are  already 
too  far  apart  for  such  an  operation  it  may  be  facili- 
tated by  giving  them  greater  amplitudes  in  their 
vibratory  notions.  This  phenomenon  occurs  in  the 
case  of  the  carbon  filament  of  the  old-style  electric 
lamp.  When  cold,  and  first  connected  to  the  electric 
light  mains,  it  offers  a  larger  resistance  than  it  does  a 
moment  later  when  it  is  heated  by  the  current. 

Any  conductor  is  heated  by  an  electrical  current. 
A  stream  of  electrons  can  only  be  passed  through  a 
conductor  as  the  result  of  an  expenditure  of  energy 
upon  the  part  of  the  system  which  establishes  or 
maintains  the  potential.  During  the  passage  of  a 
current  the  potential  energy  of  the  source  is  con- 
verted into  kinetic  energy  of  the  carriers  of  the  elec- 


CONDUCTION  THROUGH  SOLIDS  73 

tricity — the  electrons,  in  the  case  of  solids.  These 
by  their  impacts  transfer  to  the  intervening  atomic 
structures  the  energy  which  they  have  acquired. 
Heat  always  results  and  sometimes  light.  In  con- 
duction through  solids,  however,  light  is  always  an 
indirect  result  of  the  increased  thermal  agitation  and 
is  not  the  direct  result  of  recombinations  of  electrons 
with  positive  atomic  structures,  as  it  is  in  the  case  of 
conduction  through  gases.  Light  occurs  as  the  tem- 
perature rises,  and  even  melting  may  occur  if  suffi- 
cient energy  is  expended  in  the  conductor. 

Many  degrees  below  the  melting  temperature, 
however,  when  the  solid  is  red  hot  or  incandescent, 
there  is  evident  a  phenomenon  which  well  corrobo- 
rates some  of  the  statements  made  above.  Suppose 
we  have  a  wire,  or  rather  a  portion  of  it,  hi  an  evac- 
uated vessel,  as  in  the  case  of  an  incandescent  lamp 
bulb,  and  heat  the  wire  by  an  electric  current.  As 
the  temperature  increases  the  violence  of  the  motions 
of  the  electrons,  which  serve  for  conduction,  also  in- 
creases. Remember  that  these  motions  are  hap- 
hazard although  they  have  a  component  in  the  di- 
rection of  the  positive  plate.  The  progress  of  an 
electron  along  its  course  resembles  that  of  the  golf 
ball  of  an  erratic  but  powerful  driver,  for  more  and 
more  frequently  as  the  temperature  rises  will  some 
electrons  be  driven  out  of  bounds.  Those  with  suffi- 
cient energy  and  the  proper  direction  of  flight  pass 
beyond  the  influence  of  the  nuclei  of  the  surface 
atoms  and  appear  in  the  space  beyond  as  free  or  dis- 
lodged electrons.  An  electron  'which  is  emitted  in 
this  way  is  sometimes  called  a  "thermion." 


74  WITHIN  THE  ATOM 

Its  behaviour  is  quite  analogous  to  that  of  a  mole- 
cule of  a  liquid.  We  know  that  evaporation  is  in- 
creased as  the  temperature  of  a  liquid  is  raised  and 
are  inclined  to  think  that  it  is  restricted  by  enclos- 
ing the  liquid.  In  a  partly  filled  bottle,  however, 
evaporation  proceeds  just  as  it  would  if  the  bottle 
were  open  except  for  the  fact  that  the  flighty  mole- 
cules which  evaporate  have  no  place  to  go  other  than 
that  immediately  above  the  liquid.  Here  they  soon 
become  so  congested  that  in  dodging  each  other  some 
of  them  get  directed  back  toward  the  liquid  surface. 
Striking  that  surface  they  take  up  again  the  normal 
routine  of  molecules  hi  a  liquid.  If  the  temperature 
is  maintained  constant  a  condition  of  so-called  sta- 
tistical equilibrium  is  soon  reached  in  which  there  are 
just  as  many  molecules  evaporating  each  second  as 
there  are  condensing  back  into  liquid  form.  The 
same  sort  of  a  statistical  equilibrium  exists  when 
electrons  are  being  thermionically  emitted  from  a 
heated  wire  in  a  very  highly  evacuated  space. 

The  equilibrium  is  displaced,  however,  if  another 
wire  or  plate  is  inserted  in  the  vessel  and  made  posi- 
tive with  respect  to  the  heated  wire  by  proper  con- 
nection to  a  battery  or  dynamo.  Then,  the  electrons 
stream  across  the  space  to  the  positive  plate,  pass  to 
the  positive  terminal  of  the  battery  and  there  ap- 
pease to  some  extent  the  unsatisfactions  which  the 
activity  of  the  battery  elements  manifest.  At  the 
same  time  other  electrons  from  the  battery  pass 
along  a  wire  to  the  heated  electrode  and  thus  main- 
tain in  it  a  normal  supply  of  electrons. 


CONDUCTION  THROUGH  SOLIDS 


75 


This  phenomenon  was  discovered  by  Edison  many 
years  ago  although  it  was  about  thirty  years  before 
efficient  application  was  made  of  the  principles  in- 
volved. Today  it  is  widely  used  in  wire  and  wireless 
communication,  and  also  in  electrical  measurements 
in  different  types  of  industry,  for  the  principle  has 
been  applied  to  the  construction  of  an  amplifier  of 
electrical  effects  which  is  a  veritable  marvel  of  effi- 
ciency and  delicacy. 


The  Thermionic  Vacuum  Tube.  Electrons  emitted  by  a  heated 
filament,  F,  are  drawn  across  a  highly  evacuated  space  to  a 
plate,  P.  The  stream  is  very  sensitive  to  changes  in  the  electrical 
potential  of  the  grid,  G.  The  device  is  widely  used  in  the  Bell 
System  as  an  amplifier  of  telephone  currents. 

It  is  evident  that,  by  the  thermionic  emission  of 
electrons  at  a  heated  electrode,  electrons  are  secured 
for  the  conduction  of  electricity  through  a  vacuum. 
By  the  introduction  of  a  third  electrode  the  stream 
may  be  controlled  with  an  inappreciable  expenditure 
of  energy.  The  result  is  that  a  very  feeble  electrical 
effect  may  manifest  itself  by  a  very  pronounced 


76  WITHIN  THE  ATOM 

change  in  the  current  which  passes  through  the 
vacuum.  A  device  of  this  form  is  the  "audion" — so- 
called  by  DeForest  who  introduced  the  third  or  con- 
trolling electrode.  The  combination  of  picture  and 
diagram  of  Fig.  3  shows  its  practical  features.1 

We  leave  this  phenomenon,  however,  to  continue 
our  discussion  of  electrical  currents  in  wires  and  to 
develop  some  ideas  which  are  essential  to  the  later 
text.  Except  at  high  temperatures,  where  the 
electrons  may  be  "boiled  out,"  the  course  of  the 
electrons  is  entirely  controlled  by  the  wire.  Wires 
serve  much  like  pipes  for  the  guided  flow  of  electrons 
and  thus  permit  distinct  streams  of  electrons  to  be 
brought  very  close  to  one  another  without  merging. 

This  possibility  is  of  great  practical  importance 
since  parallel  streams  of  electrons  tractate.  The 
tractation  of  parallel  electron  streams  results  in  a 
tractation  of  the  wires  in  which  these  streams  are 
confined.  Streams  in  opposite  directions  pellate  and 
hence  the  wires  which  carry  them  are  urged  apart. 
If  streams  are  at  right  angles  there  is  no  reaction  be- 
tween them.  The  phenomena,  unfortunately,  are 
as  completely  without  explanation  as  are  the  funda- 
mental phenomena  of  the  tractation  of  proton  and 
electron  or  the  pellation  of  two  electrons  or  two  pro- 
tons. 

The  effect  depends  for  its  magnitude  upon  the 
length  of  the  wires  which  are  parallel,  the  intensities 
of  the  currents,  and  the  distance  between  the  wires. 

The  device  has  been  highly  developed  both  in  structure  and 
application  by  the  research  physicists  and  communication  en- 
gineers of  the  Bell  Telephone  System  and  of  the  General  Electric 
Company. 


CONDUCTION  THROUGH  SOLIDS 


77 


The  greater  the  lengths  which  are  parallel  and  the 
greater  the  currents,  that  is  the  greater  the  numbers 
of  electrons  which  stream  through  the  wires  each 
second,  the  greater  is  the  effect  of  attraction.  It 
therefore  happens  that  the  effect  may  be  enhanced 
by  arranging  each  wire  in  the  form  of  a  coil,  the  suc- 
cessive turns  of  which  will  carry  the  same  electron 
stream.  Two  coils  of  this  solenoidal  form  are  shown 
in  Fig.  4.  If  they  are  supported  so  as  to  be  free  to 

Attraction 


Battery 


Battery 


FIG.  4 


Attraction  of  wires  which  cany  parallel  streams  of  electrons  in 
the  direction  indicated  by  the  arrows. 

move  it  is  found  that  they  rotate  so  that  their  loops 
are  parallel  and  at  the  same  time  they  move  closer 
together  so  that  they  tend  to  form  one  long  con- 
tinuous solenoid,  the  turns  of  which  all  carry  parallel 
electron  streams. 

The  effect  is  very  greatly  increased  by  winding  the 
coils  on  cores  of  so-called  magnetic  material,  for  ex- 
ample, iron,  cobalt,  nickel,  or  certain  alloys  for  which 
the  electronic  configurations  are  generally  similar  to 
those  of  these  elements.  The  effect  of  the  currents 
in  the  coils  upon  the  atoms  or  molecules  of  the  mag- 
netic cores  is  easily  explainable  if  we  assume  rota- 


78 


WITHIN  THE  ATOM 


tions  for  some  or  all  of  the  planetary  electrons  of  an 
atom  of  a  magnetic  substance.  Suppose  some  of 
the  electrons  are  revolving  about  the  nucleus.  They 
constitute  a  stream  of  electrons  around  a  loop  just 
as  really  as  do  the  streams  which  travel  the  larger 
loops  of  the  solenoids  which  we  have  been  consider- 
ing. 

Each  molecule  or  atom  of  a  magnetic  substance 
will  then  act  like  a  current-carrying  loop  and  will 
tend  to  place  itself  so  that  its  loop  lines  up  with  other 

Attraction 


Iron* 


^x 


SPole 


FIG.  5 


NPole 


f=  Direction  of 

Electron  Rotation 


Equivalence  of  a  bar  magnet  and  a  current-carrying  solenoid  in 
phenomena  of  attraction. 

current-carrying  loops.  The  effect  of  the  current  in 
the  solenoid  is  to  orient  the  individual  atoms  or  mole- 
cules of  the  core  so  that  as  many  as  possible  of  their 
loops  shall  be  parallel  to  those  of  the  solenoid. 
Under  this  condition  the  core  is  said  to  be  magnet- 
ized, and  the  combination  of  core  and  exciting  sole- 
noid is  called  an  electro-magnet. 

The  orientation  which  the  molecules  of  the  core 
acquire  by  virtue  of  the  magnetizing  current  in  the 
solenoid  is  retained  with  more  or  less  tenacity  after 
the  current  has  ceased  to  flow.  The  core  is  thus 
made  into  a  more  or  less  permanent  magnet.  If  its 


CONDUCTION  THROUGH  SOLIDS 


79 


ends  are  marked  for  reference  and  it  is  then  with- 
drawn from  the  solenoid  it  will  be  found  to  replace  a 
current-carrying  solenoid  and  generally  to  behave  as 
if  it  were  a  coaxial  series  of  current-carrying  loops. 
(See  Fig.  5.)  In  all  phenomena  of  mutual  attrac- 
tion or  repulsion,  magnets  and  current-carrying 
solenoids  are  equivalent. 


FIG.  6 

Interaction  of  magnetic  field  and  electron  stream.  The  large 
current-carrying  loop  and  the  solenoid  tend  to  place  themselves 
coaxially.  The  effect  is  that  the  wire,  AB,  carrying  the  electron 
stream  is  pushed  sidewise  across  the  magnetic  field  between  N 
and  S. 

In  the  case  of  magnetic  materials  we  picture  some 
or  all  of  the  planetary  electrons  as  engaged  in  circu- 
lar or  elliptical  motions.  Adjacent  molecules  would 
then  tend  to  orient  themselves  so  as  to  have  their 
current  loops  in  parallel.  We  might  therefore  ex- 
pect that  in  any  piece  of  iron  the  molecules  would 
of  their  own  action  have  assumed  such  similar 
orientations  as  to  have  made  the  piece  of  iron  a  mag- 
net. Such,  however,  is  not  the  case.  The  mole- 


80  WITHIN  THE  ATOM 

cules  have  haphazard  orientations,  as  may  be  veri- 
fied by  placing  one  piece  of  ordinary  iron  near 
another  and  noticing  that  there  is  no  attraction  or 
repulsion  as  there  would  be  if  the  molecular  cur- 
rents were  not  flowing  "every  which  way."  The  ex- 
planation is  that  the  molecules  have  already  formed 
themselves  into  a  large  number  of  small  and  fairly 
stable  groups.  For  this  reason  heating  and  jarring, 
which  increase  molecular  agitation,  facilitate  the 
process  of  magnetization  of  an  electromagnet  or 
the  process  of  "self-demagnetization"  by  which  its 
molecules  reform  self-satisfied  groups  which  neutral- 
ize each  other's  external  effects. 

All  so-called  magnetic  phenomena  are  merely  the 
interactions  of  parallel  streams  of  electrons.  As  far 
as  possible  current-carrying  loops  interact  so  as  to 
place  themselves  parallel  and  coaxial  and  to  have 
electron  streams  in  the  same  sense,  e.g.  clockwise,  or 
counter-clockwise,  when  viewed  from  a  common 
point,  not  between  the  two  loops.  An  application 
of  this  law,  which  is  of  importance  in  our  later  dis- 
cussion, is  shown  in  Fig.  6.  If  a  portion  of  a  current- 
carrying  loop  of  large  size  is  placed  between  two 
coaxial  coils,  which  are  carrying  currents  in  the  same 
sense,  then  the  portion  of  the  large  loop  is  urged 
along  a  line  at  right  angles  to  the  axis  of  the  fixed 
coils  in  a  direction  depending  upon  the  direction  of 
the  current.  The  coaxial  coils  may  contain  cores 
and  be  electromagnets  or  may  be  replaced  by  per- 
manent magnets  without  prejudice  to  the  experi- 
ment. 

Usually  there  is  said  to  be  a  magnetic  field  of  force 


CONDUCTION  THROUGH  SOLIDS 


81 


between  the  two  coils  or  magnets.  The  direction  of 
such  a  field  is  taken  as  that  in  which  the  north-seek- 
ing end  of  a  compass  needle  would  point.  The  direc- 
tion of  deflection  for  the  stream  of  electrons  in  the 
large  loop  will  then  be  related  to  this  direction  of  the 
magnetic  field  and  to  the  direction  of  the  electron 
stream  as  is  the  thumb  of  one's  right  hand  to  the 


FIG.  8 

The  relative  directions 
of  magnetic  field,  F,  of 
the  motion,  M,  of  a  con- 
ductor, and  of  the  in- 
duced electron  stream, 
C,  in  the  conductor. 


FIG.  7 


The  relative  directions  of  a  magnetic  field,  F,  of  an  electron 
stream,  C,  and  of  the  motion,  M,  of  the  stream  relative  to  the 
field. 

fore  and  center  fingers,  respectively,  when  all  three 
digits  point  at  right  angles  to  each  other. 

In  the  application  of  this  rule,  as  pictured  in  Fig.  7, 
it  must  be  remembered  that  so  far  as  concerns  this 
phenomenon  a  stream  of  positive  ions  is  equivalent 
to  a  stream  of  electrons  in  the  opposite  direction. 

UNIVERSITY  OF  fcAUFORNIA 
DEPARTMENT  OF  CIVIL  ENGINEERJNC 


crv 


82  WITHIN  THE  ATOM 

Parallel  currents  undergo  mutual  deflections  at 
right  angles  to  their  directions.  Does  such  deflec- 
tion alter  the  currents?  Always,  for  every  physical 
action  has  an  equal  and  opposite  reaction.  The 
electron  streams  are  momentarily  affected  by  their 
deflection  in  such  a  manner  as  to  oppose  the  change. 
If  the  currents  in  two  parallel  wires  are  in  such  direc- 
tions as  to  cause  an  attraction  of  the  wires,  then 
during  their  mutual  approach  the  currents  are  mo- 
mentarily decreased. 

For  simplicity  let  us  concentrate  our  attention  on 
a  single  current,  choosing  that  of  the  portion  of  the 
large  loop  of  Fig.  6  which  we  know  is  deflected  across 
the  magnetic  field  between  the  two  solenoids.  The 
wire  is  deflected  in  the  direction  given  by  the  right- 
hand  rule  of  Fig.  7.  If  there  were  flowing  in  it  a 
stream  of  electrons  in  the  opposite  direction  there 
would  be  a  tendency  to  the  opposite  deflection.  If 
the  actual  deflection  which  takes  place  is  to  be  ac- 
companied by  a  reaction,  this  reaction  may  be  ac- 
complished by  the  setting  up  of  an  opposing  stream 
of  electrons.  Such  a  counter  stream  will  result  in  a 
reduction  in  the  net  number  of  electrons  which  are 
being  transferred  along  the  wire.  The  current, 
therefore,  is  reduced  momentarily,  that  is  as  long  as 
there  is  a  deflection  of  wire. 

Now  suppose  that  the  wire  carries  no  current  and 
that  by  some  external  means  it  is  caused  to  move 
across  the  field  between  the  two  solenoids  of  Fig.  6. 
Let  its  direction  of  motion  be  the  same  as  before. 
The  original  stream  of  electrons  no  longer  exists  but 
the  induced  stream  comes  momentarily  into  exist- 


CONDUCTION  THROUGH  SOLIDS  83 

ence  just  as  before  and  its  direction  is  such  as  to  op- 
pose the  cause  inducing  it. 

The  relations  of  direction  of  motion,  direction  of 
field,  and  direction  of  the  induced  stream  of  electrons 
will  be  identical  with  that  pictured  in  Fig.  7,  except 
that  the  direction  of  the  electron  stream  is  reversed. 
By  using  the  left  hand,  however,  as  shown  in  Fig.  8, 
the  directions  may  be  represented  by  the  same  sym- 
bols as  before.  We  may  call  the  left-hand  relations 
those  for  the  induction  of  electronic  streams  and  the 
right-hand  relations  those  for  the  deflection  of  elec- 
tronic streams. 

It  is  this  phenomenon  of  the  induction  of  elec- 
tronic streams  which  is  used  to  such  industrial 
advantage  in  the  so-called  "generation  of  electricity" 
for  power  purposes.  By  rotating  machinery,  coils  of 
wire  are  kept  in  motion  across  magnetic  fields  and 
thus  there  are  obtained  streams  of  electrons  which 
may  be  guided  by  wires  to  points  where  the  energy 
of  the  moving  electrons  may  be  utilized. 

The  utilization  may  involve  the  phenomenon  of 
the  attraction  of  parallel  streams  of  electrons  in 
motors  where  the  electron  streams  cause  coils  of  wires 
to  rotate  relative  to  electromagnets.  In  many  cases 
the  utilization  involves  the  release  of  the  energy  of 
the  electron  streams  in  the  form  of  the  heat  and 
light  which  results  from  the  impeded  progress  of  the 
electrons  through  wires  which  offer  high  resistance. 


CHAPTER  VIII 

THE  PROOF  FOR  THE  EXISTENCE  OF  AN  ELECTRON 

OUR  knowledge  of  the  interactions  of  magnets 
dates  from  Gilbert,  the  Elizabethan  physician;  our 
knowledge  of  the  interactions  of  a  magnet  with  an 
electric  current,  or  of  current  with  current,  started 
with  Oersted  in  the  early  nineteenth  century;  and 
our  knowledge  of  electronic  structures  has  been  al- 
most entirely  a  twentieth -century  development.  It  is 
natural,  therefore,  to  say  that  electric  currents  pro- 
duce magnetic  effects.  Magnetic  properties  were  at- 
tributed to  currents  hi  order  to  explain  their  inter- 
actions. Today,  however,  we  incline  toward  the 
explanation  of  the  properties  of  so-called  magnetic 
substances  in  terms  of  revolutions  of  the  electrons 
within  their  atoms,  although  we  do  not  know  defi- 
nitely the  nature  of  these  revolutions. 

The  chemical  properties  of  atoms,  which  were  dis- 
cussed in  Chapter  III  in  connection  with  the  periodic 
table,  are  most  easily  explained  if  we  assume  the 
planetary  electrons  to  be  located  in  fairly  definite 
positions.  The  magnetic  properties  are  best  vizual- 
ized  if  we  assume  electrons  to  be  rotating.  The 
emission  of  light,  as  we  shall  see  later,  requires  that 
the  electrons  shall  be  in  rotation  and  that  their  orbits 
shall  change  under  various  conditions.  So  far  no 

84 


THE  PROOF  FOR  AN  ELECTRON     85 

satisfactory  picture  has  been  presented,  although  for 
the  simpler  atoms  of  hydrogen  and  helium  there  have 
been  suggested  atomic  models  which  would  have 
properties  in  agreement  with  those  observed  for 
these  substances. 

Although  we  are  in  ignorance  of  the  exact  form 
of  the  paths  pursued  by  the  electrons  in  atoms  we  are 
perhaps  justified  in  assuming  that  rotations  do  occur 
and  in  explaining  so-called  magnetic  attractions  by 
the  interactions  of  electrons  which  are  moving  in 
parallel  paths.  If  the  paths  are  at  right  angles  there 
are  no  attractions.  For  intervening  directions  the 
attraction  depends  upon  the  components  of  the  mo- 
tions which  are  parallel.  The  idea  of  a  component 
is  easily  grasped  when  one  realizes  that  if  two  bodies 
are  not  going  in  directions  exactly  at  right  angles  to 
each  other,  they  must  to  some  extent  be  going  in  the 
same  direction,  and,  with  equal  truth,  to  some  other 
extent  at  right  angles  to  each  other.  The  extent  to 
which  one  body  is  moving  in  the  same  direction  with 
a  second  is  the  component  of  the  motion  of  the  first 
in  the  direction  of  the  second. 

The  magnetic  attraction  which  occurs  between 
electrons  with  components  of  motion  in  the  same 
direction  is  very  probably  one  reason  why  such  mu- 
tually repulsive  entities  as  electrons  can  form  a  group 
about  an  inner  nucleus.  The  magnetic  attraction 
may  partially  offset  the  tendencies  of  the  electrons 
to  pellate  and  may  thus  assist  the  nucleus  in  retain- 
ing them  within  atomic  limits.  It  may  also  be  that 
the  protons  and  electrons  within  the  nucleus  are  re- 
strained from  flying  apart  by  similar  attractions. 


86  WITHIN  THE  ATOM 

To  make  these  attractive  forces  commensurable 
with  the  natural  repulsions  of  similar  electrical  ele- 
ments would  require  high  speeds  for  the  elements 
which  are  rotating  and  thus  represent  large  energies. 
This  would  fit  with  the  observed  facts  as  to  the  high 
energies  possessed  by  alpha  and  beta  particles.  The 
actual  geometry  of  the  atomic  nucleus,1  however,  is 
far  in  the  speculative  twilight,  although  present 
scientific  progress  is  so  rapid  that  the  whole  matter 
might  well  be  explained  within  a  few  years. 

In  dealing  with  the  interactions  of  electrical  cur- 
rents it  is  usual  to  speak  as  if  one  current  acted  on 
the  other  and  to  neglect  the  reaction  of  the  second 
on  the  first.  To  the  acting  current  we  attribute  a 
magnetic  field  and  then  speak  of  this  field  as  acting 
upon  the  current  in  which  we  are  interested.  It  is 
in  this  terminology  that  one  will  find  described  the 
classical  experiments  which  established  the  electron 
theory  with  which  modern  science  starts.  Through- 
out all  the  original  reports  one  will  find  the  idea  of 
fields  of  force,  not  only  magnetic  but  so-called  elec- 
trostatic fields.  The  latter  are  the  regions  near 
charged  bodies  and  the  direction  of  the  field  is  taken, 
unfortunately,  as  that  in  which  a  positive  charge 
would  move. 

By  applying  magnetic  and  electrostatic  fields  of 
force  to  the  streams  of  particles  which  are  expelled 

1  The  most  recent  evidence  is  that  of  C.  J.  Darwin  (February, 
1921)  who  worked  with  Professor  Rutherford  in  the  latter's 
experiments  on  the  collision  of  alpha  particles  with  hydrogen 
nuclei.  The  evidence  seems  to  support  the  idea  that  an  alpha 
particle  has  a  shape  something  like  a  plate  or  disc  with  a  diameter 
of  2.7  x  10-"  cm.  The  evidence  comes  from  experiments  simi- 
lar to  those  described  on  page  113. 


THE  PROOF  FOR  AN  ELECTRON     87 

from  radioactive  bodies,  there  was  obtained  the  first 
information  that  these  were  streams  of  particles  or 
corpuscles  instead  of  radiations  as  intangible  and 
imponderable  as  those  of  light.  In  a  magnetic  field 
a  stream  of  alpha  particles  is  deflected  in  the  opposite 
direction  from  a  stream  of  beta  particles,  and  the 
same  is  true  for  an  electrostatic  field  such  as  exists 
between  two  oppositely  charged  plates.  The  proof 
of  the  existence  of  electrons,  however,  was  reached 
largely  by  the  study  of  so-called  "cathode  rays." 

The  origin  of  the  latter  phrase  is  explained  as  fol- 
lows: In  the  study  of  electrolysis,  that  is  the  con- 
duction of  electricity  through  liquids  which  was  dis- 
cussed in  Chapter  II,  two  terminal  plates  are  inserted 
in  the  liquid.  The  positive  plate  was  called  the 
anode  and  the  negative  the  cathode  since  it  was 
assumed  that  electricity  flowed  up  to  one  and  down 
to  the  other.  The  terms  have  been  retained  and  ap- 
plied to  the  terminal  plates  in  conduction  through 
gases. 

We  remember  also  from  our  discussion  of  gases 
that  electrons  are  liberated  at  the  negative  plate 
when  there  is  a  sufficiently  severe  bombardment  of 
this  plate  by  positive  ions.  If  the  tube  containing 
the  gas  through  which  conduction  is  taking  place  is 
not  too  highly  exhausted  a  relatively  large  number  of 
gas  molecules  are  present  and  may  be  ionized.  On 
the  other  hand,  if  it  is  not  so  little  exhausted  that  a 
gaseous  molecule  is  stopped  by  collision  before  it 
travels  a  distance,  representing  a  potential  difference, 
sufficient  to  acquire  the  necessary  energy,  then  the 
impacts  of  the  positive  ions  will  liberate  electrons 


88  WITHIN  THE  ATOM 

from  the  cathode.  These  shoot  off  into  space,  re- 
pelled by  the  negative  plate  from  which  they  are 
derived.  Their  energy  comes  from  the  battery 
which  keeps  the  cathode  negative,  by  forcing  upon 
it  electrons  far  in  excess  of  its  possibilities  of  getting 
rid  of  them.  Electrons  may  be  freed  from  the 
cathode  and  so  made  available  for  conduction 
through  the  tube  only  by  the  bombardment  of  the 
positive  ions  (or  by  other  agencies,  like  ultra-violet 
light,  which  do  not  concern  the  present  case) . 


FIG.  9 

Cross-section  of  apparatus  for  examination  of  cathode  rays. 
The  cathode  stream  from  C  passed  through  the  tubular  anode,  A. 
It  was  deflected  by  the  magnetic  field  into  the  vessel,  V,  for 
which  an  electroscope,  E,  then  indicated  a  negative  charge. 

The  result  is  a  steady  stream  of  electrons,  flying 
from  the  cathode  with  velocities  which  may  be  al- 
most as  enormous  as  that  of  light.  These  constitute 
the  "cathode  rays,"  as  they  were  first  called.  Where 
they  impinge  on  the  glass  of  the  tube  they  cause  it 
to  phosphoresce,  and  thus  their  paths  may  be  traced. 
Many  of  the  electrons  travel  straight  for  the  positive 
terminal,  or  anode.  If  the  latter  is  made  hollow,  or 
perforated,  many  will  pass  straight  through  with  al- 


THE  PROOF  FOR  AN  ELECTRON     89 

most  no  regard  for  its  attracting  excess  of  protons 
for  they  are  going  too  fast  to  stop.  The  result  is 
that  a  "beam"  of  cathode  rays  is  available  for  experi- 
mental study  in  the  space  beyond  the  anode,  as 
shown  in  Fig.  9. 

Through  this  space  the  beam  travels  straight 
except  as  deflected,  for  example  by  magnets  set  out- 
side the  tube  so  as  to  establish  a  magnetic  field  at 
right  angles  to  the  stream.  In  one  of  the  original 
experiments  of  J.  J.  Thomson  the  beam  was  deflected 
into  the  hollow  metal  vessel,  V,  shown  in  the  figure. 
The  direction  of  deflection  indicated  that  the  beam 
was  a  stream  of  negative  particles.  Further  evi- 
dence came  from  the  charge  which  the  beam  gave  to 
the  vessel  V,  for  the  latter  was  found  to  be  negative. 

You  will  remember,  however,  that  it  should  also 
be  possible  to  deflect  the  beam  by  placing  above  and 
below  it  oppositively  charged  plates.  If  the  upper 
plate  is  made  positive  the  stream  of  electrons  should 
be  attracted  toward  it  and  repelled  by  the  lower 
negative  plate.  By  subjecting  the  beam  to  this  in- 
fluence the  effect  of  the  magnetic  field  can  be 
counteracted,  provided  that  there  is  maintained  a 
certain  relation  for  the  intensities  of  the  electrostatic 
field  which  deflects  upward  and  the  magnetic  which 
deflects  downward.  It  happens  that  the  ratio  of 
these  intensities  depends  only  upon  the  velocity  with 
which  the  particles  in  the  stream  are  moving.  By 
such  a  balancing  of  deflections,  therefore,  Thomson 
was  able  to  determine  the  velocity  of  the  particles. 
His  apparatus  is  shown  in  Fig.  10. 

Up  to  this  time  the  electron  was  unknown  and 


90  WITHIN  THE  ATOM 

electricity  had  been  measured  in  other  units  than 
this  natural  unit.  He  next  sought  in  terms  of  exist- 
ing units  to  measure  the  charge  which  each  particle 
carried.  However,  it  wag  not  then  known  how  to 
measure  this  quantity  directly,  and  the  method  he 
devised  gave  the  relation  of  the  charge  on  the  particle 
to  its  mass  (inertia). 

He  found  this  ratio  by  observing  the  deflection 
which  was  produced  when  only  the  electrostatic  field 
was  active.  Each  electron  in  the  stream  behaves 


•Magnet 


Side  View  Cross  Section  pt  XXf 

FIG.  10 

Apparatus  used  by  J.  J.  Thomson  for  determining  properties  of 
cathode  rays.  Electrons  from  C  pass  through  A  to  the  screen,  P. 
The  magnets  and  the  plates  deflect  the  stream  up  or  down, 
depending  on  their  respective  polarities. 

like  a  bullet  shot  in  a  horizontal  line  and  the  plate 
toward  which  it  is  attracted  acts  like  the  earth  with 
its  gravitational  pull.  The  constant  pull  gives  the 
particle  an  acceleration  toward  the  plate  just  as  in 
the  case  of  a  bullet  and  the  earth.  The  acceleration, 
however,  depends  upon  the  charge,  for  it  is  by  virtue 
of  the  charge  that  the  particle  is  attracted  toward  the 
plate,  and  upon  the  mass  or  unwillingness  to  be  ac- 
celerated. From  the  horizontal  and  vertical  dimen- 
sions of  the  parabolic  path  which  the  particle  pur- 
sued Thomson  determined  the  ratio  of  its  charge  to 


THE  PROOF  FOR  AN  ELECTRON     91 

its  mass.  It  was  found  to  be  about  1700  times  the 
similar  ratio  for  the  hydrogen  ion  which  takes  part 
in  electrolytic  conduction. 

An  approximate  value  for  the  mass  of  the  particle 
in  a  cathode  ray  was  then  obtained  upon  the  assump- 
tion that  the  ion  of  hydrogen  is  essentially  the  same 
in  mass  as  the  hydrogen  atom  and  that  the  charge  of 
electricity  which  it  carries  is  equal  but  opposite  in 
kind  to  that  of  the  particle  under  examination. 
Upon  this  assumption  the  mass  of  the  unknown 
particle  was  obtained  as  one-seventeen-hundredth  of 
a  hydrogen  atom,  since  its  mass  must  be  that  much 
smaller  in  order  to  make  the  ratio  of  charge  to  mass 
correspondingly  larger. 

Methods  for  determining  the  unknown  charge  on 
the  particle  were  soon  devised  and  one  by  Townsend 
was  widely  used.  The  latter  knew  that  not  all  the 
gas  which  escapes  at  an  electrode  in  an  electrolytic 
action,  like  that  described  at  the  end  of  Chapter  VI, 
is  composed  of  neutral  uncharged  molecules.  Once 
in  a  million  times  or  so  a  molecule  may  carry  away  a 
charge,  the  result,  apparently,  of  hasty  combination. 
Whether  the  molecule  gets  out  into  free  space  with 
one  too  few,  or  one  too  many,  electrons  is  not  acci- 
dental but  is  characteristic  and  depends  upon  the 
electrolyte  from  which  the  gas  rises. 

If  the  air  above  the  electrolyte  contains  moisture, 
that  is  molecules  of  water  wandering  about  like 
molecules  of  ordinary  gas,  then  the  charged  mole- 
cules act  as  centers  of  attraction  for  the  water  mole- 
cules. The  latter  aggregate  about  the  charges, 
forming  small  drops  which  appear  as  a  cloud.  The 


92  WITHIN  THE  ATOM 

natural  assumption  is  that  in  such  a  condensation 
the  number  of  droplets  is  equal  to  the  number  of 
centers  about  which  drops  can  form.  Townsend 
therefore  calculated  the  number  of  drops  in  the 
cloud,  measured  the  electrical  charge  involved,  and 
thus  found  the  charge  per  drop,  that  is  the  desired 
elemental  charge. 

The  number  of  drops  was  obtained  by  calculating 
the  amount  of  water  in  each  drop  and  then  dividing 
this  into  the  total  weight  of  the  entire  cloud.  The 
latter  was  found  by  passing  the  cloud  through  tubes 
filled  with  chemicals,  which  took  up  the  water,  and 
observing  their  increase  in  weight.  The  volume  of 
the  drops  was  calculated  on  the  basis  of  earlier  work 
by  Stokes  who  had  expressed  quantitatively  the  law 
for  the  descent  under  gravity  of  small  drops.  The 
smaller  the  drop  the  more  slowly  does  it  fall.  Such 
drops  as  formed  the  clouds  with  which  Townsend 
worked  will  take  about  half  a  minute  to  fall  through 
an  inch  of  air.  By  observing  the  rate  of  fall  of  the 
entire  cloud  the  average  size  of  its  drops  could  be 
computed  and  hence  their  weight  obtained. 

To  measure  the  total  charge  which  the  cloud  car- 
ried there  was  used  a  calibrated  electroscope,  or  elec- 
trometer, as  it  is  called.  This  instrument  has  proved 
of  great  usefulness  in  most  of  the  experiments  which 
have  led  to  the  present  state  of  our  knowledge  of 
electrons  and  radioactive  substances.  In  simplest 
form  it  consists  of  a  vertical  metal  strip  to  which  is 
attached  a  light  gold  leaf.  The  metal  strip  is  insu- 
lated from  the  protecting  case  through  which  it  pro- 
jects to  an  external  knob. 


THE  PROOF  FOR  AN  ELECTRON     93 

If  a  charged  body  is  brought  in  contact  with  the 
knob  there  is  a  transfer  of  electrons  either  to  the 
knob  or  from  it.  Let  us  suppose  the  body  negative. 
Then  electrons  pass  to  the  knob  and  because  of  mu- 
tual repulsions  pass  down  into  the  metal  strip  and 
its  gold  leaf.  There  their  repulsions  result  in  the  de- 
flection of  the  gold  leaf  which  stands  out  at  an  angle 
from  the  vertical.  When  the  charged  body  is  re- 
moved some  of  the  electrons  at  the  bottom  of  the 
strip  are  repelled  back  to  the  knob  and  the  leaf  drops 
a  little  to  a  new  and  final  position  which  it  maintains 
except  as  the  charge  on  the  system  is  neutralized  by 
stray  ions  in  the  air  about  it. 

If  now  another  charged  body  is  brought  near  but 
not  into  contact  with  the  knob  two  different  actions 
are  possible.  If  the  new  body  is  negative  the 
electrons  are  again  repelled  into  the  extremities  of 
the  strip  and  gold  leaf  and  there  results  an  increased 
deflection.  On  the  other  hand  if  the  new  body  is 
positive  its  excess  of  protons  attracts  electrons  to- 
ward the  knob  and  the  number  at  the  bottom  of  the 
system  are  no  longer  sufficient  to  maintain  the 
former  deflection  so  that  the  leaf  falls  back. 

The  same  effect  is,  of  course,  produced  if  a  charge 
is  added  to  the  gold  leaf  system  by  direct  contact  of 
the  charged  body  with  the  knob.  The  only  difficulty 
is  that  if  the  charge  is  of  opposite  kind  to  that  al- 
ready on  the  system  it  may  neutralize  that  charge, 
allowing  the  leaf  to  drop,  and  instantly  recharge  the 
electroscope  with  the  opposite  kind  of  electricity, 
causing  the  leaf  again  to  stand  out  from  its  support. 
By  proper  care,  however,  the  change  in  deflection  of 


94  WITHIN  THE  ATOM 

the  gold  leaf  may  be  made  not  only  to  indicate  the 
kind  of  charge  but  also  to  measure  its  amount.  By 
such  a  method  Townsend  determined  the  total 
charge  on  his  cloud. 

The  series  of  experiments  described  above  were 
sufficient  to  establish  the  fact  that  cathode  rays  are 
streams  of  negatively  charged  particles,  each  with  a 
charge  like  that  of  the  hydrogen  ion  in  electrolysis, 
and  a  mass  about  one  1700th  of  that  ion,  and  also  to 
determine  in  terms  of  the  standard  units  the  charge 
on  individual  particles.  With  the  conclusion  of  this 
series  the  existence  of  the  electron  was  established. 

Experiments  of  this  character  are  obviously  com- 
plicated since  they  generally  involve  a  number  of 
necessary  subsidiary  experiments  as  well  as  mathe- 
matical formulation  and  a  careful  use  of  units.  In 
this  book  we  shall  describe  only  a  few.  One,  which 
deserves  immediate  attention,  is  Millikan's  method 
for  determining  the  value  of  an  electron  in  terms  of 
the  earlier  accepted  units  for  electrical  charge. 

Millikan's  work,  extending  from  1907  to  1917,  was 
a  series  of  ingenious  experiments,  each  more  simply 
direct  than  the  preceding  and  adapted  to  giving  more 
precise  results.  In  one  of  these,  instead  of  a  cloud, 
he  used  a  single  drop  under  conditions  which  elimi- 
nated the  properties  of  the  drop  itself  and  of  the 
medium  in  which  it  was  placed  and  gave  direct  indi- 
cations of  the  electrical  charge  which  the  drop 
carried. 

The  principal  features  of  his  apparatus  appear  in 
Fig.  11.  Between  the  two  parallel  plates,  M  and  N, 
a  droplet  was  introduced  by  spraying  oil  from  an 


THE  PROOF  FOR  AN  ELECTRON 


95 


atomizer  into  a  chamber  above.  Drops  about  one- 
ten-thousandth  of  an  inch  in  diameter  were  thus 
formed.  As  these  fell  slowly  through  the  chamber 
one  would  find  its  way  through  the  small  hole  at  p 
into  the  space  between  the  plates.  Here  it  was 
made  visible  as  a  bright  speck,  by  a  powerful  stream 
of  light,  just  as  particles  of  fine  dust  in  the  air  are 


Earth 


Earth 


FIG.  11 


Cross-section  of  Millikan's  apparatus  for  measuring  the  ele- 
mental charge  of  electricity  (the  electron) .  An  electrified  oil  drop 
between  the  plates  M  and  N  falls  or  rises,  depending  upon  the 
electrical  condition  of  these  plates,  and  this  is  controllable  by  the 
battery,  B,  and  the  switch,  S. 

made  visible  by  a  transverse  beam  of  sunlight.  Its 
motion  was  observed  through  a  small  telescope  and 
was  timed  by  a  stop  watch  or  a  chronograph. 

Between  the  plates  an  electrical  potential  was  ap- 
plied by  a  battery,  B,  so  arranged  with  switches,  S, 
as  to  permit  making  either  plate  positive  and  the 
other  negative.  The  drops  acquired  charges  by  fric- 
tion as  they  left  the  atomizer.  The  plates,  however, 


96  WITHIN  THE  ATOM 

were  not  charged  until  a  drop  was  seen  in  the  field  of 
view  of  the  telescope.  As  long  as  the  plates  remained 
uncharged  the  drop  would  fall  slowly,  about  one  thir- 
tieth of  an  inch  a  second.  Connecting  the  plates  to 
the  battery  would  result  in  a  change  of  speed.  If 
the  charge  on  the  drop  was  the  same  kind  as  that  of 
the  upper  plate  it  would  fall  more  rapidly,  but  if  op- 
posite to  that  of  this  plate  it  would  either  rise  or  re- 
main practically  at  rest,  depending  upon  whether  or 
not  the  potential  applied  to  the  plates  was  sufficient 
to  do  more  than  neutralize  the  gravitational  effect. 

The  drop  was  caused  to  rise  and  allowed  to  fall, 
alternately,  and  the  tunes  were  observed.  Some- 
times the  drop  would  suffer  collision  with  some  ion 
of  the  atmosphere  between  the  plates  and  then  be- 
cause of  its  changed  electrical  condition  its  time  of 
rise  would  be  changed,  but  its  time  of  fall,  when  the 
plates  were  uncharged,  would  not  change.  A  fair 
supply  of  ions  for  such  collisions  were  provided  by 
bringing  radium  near  the  apparatus  or  by  exposing 
the  air  between  the  plates  to  X-rays. 

The  drop  could  be  caused  to  collide  with  either 
positive  or  negative  ions  by  the  following  method: 
Suppose  it  was  desired  to  add  positive  charges  to  the 
drop.  It  would  be  brought  near  the  negative  plate 
and  then  kept  from  falling  by  properly  adjusting  the 
potential.  Then  the  space  would  be  exposed  to  ion- 
izing radiations  from  the  radium.  The  negative 
ions,  thus  formed,  would  move  toward  the  positive 
plate  and  away  from  the  drop.  All  the  positive  ions, 
however,  would  move  toward  the  other  plate  and  the 
drop  would  thus  be  hi  a  veritable  shower  of  positive 


THE  PROOF  FOR  AN  ELECTRON     97 

ions.  In  this  way  the  charge  originally  held  by  the 
drop  could  be  increased  or  neutralized  and  reversed, 
if  desired. 

A  change  in  the  velocity  with  which  the  drop  rose 
would  indicate  a  change  in  the  charge  it  carried.  If 
there  is  an  elemental  charge  there  should  be  a  defi- 
nite minimum  change  in  velocity  corresponding  to 
adding  or  subtracting  this  charge  from  the  drop  and 
all  other  charges  should  be  small  exact  multiples  of 
this  minimum.  On  the  assumption  that  the  electri- 
fied condition  of  the  drop  is  due  to  a  certain  excess 
or  deficiency  of  electrons,  this  is  what  we  should  ex- 
pect, and  this  is  what  Millikan  found.  His  experi- 
ment constitutes  a  beautiful  proof  of  the  existence 
of  a  definite  elemental  quantity  of  electricity. 

By  a  proper  correlation  of  his  quantitative  data  he 
arrived  at  a  very  exact  determination  of  the  value 
of  this  elemental  charge  in  terms  of  the  usual  units 
for  measuring  electricity.  In  the  Appendix  we  shall 
consider  the  numerical  value  for  this  important 
physical  magnitude.  For  the  moment,  however,  we 
quote  an  illustration  from  Millikan  to  relate  the 
electron  to  a  familiar  magnitude.  He  says  that  the 
number  of  electrons  which  pass  every  second  through 
a  common  16-candle  power  electric-lamp  filament  is 
so  large  that  it  would  take  the  two  and  a  half  million 
people  in  Chicago,  counting  at  the  rate  of  two  each 
second,  twenty  thousand  years  of  24-hour  working 
days  to  count  an  equivalent  number. 

It  made  no  difference  how  the  electrification  was 
produced  or  the  charge  transferred.  Millikan  used 
thousands  of  drops  in  various  media,  experimenting 


98  WITHIN  THE  ATOM 

with  drops  of  non-conducting  substances  like  oil, 
poor  conductors  like  glycerin,  and  excellent  metallic 
conductors  like  mercury.  He  states  that  "in  every 
case,  without  a  single  exception,  the  initial  charge 
placed  upon  the  drop  by  the  frictional  process,  and 
all  the  dozen  or  more  charges  which  resulted  from 
the  capture  by  the  drop  of  a  larger  or  smaller  number 
of  ions,  were  found  to  be  exact  multiples  of  the 
smallest  charge  caught  from  the  air." 

His  experiments  were  a  beautiful  demonstration 
of  the  correctness  of  the  concept  of  an  electron. 
They  "placed  beyond  all  question  the  view  that  an 
electrical  charge,  wherever  it  is  found,  whether  on  an 
insulator  or  a  conductor,  whether  in  electrolytes  or 
in  metals,  has  a  definite  granular  structure,  and  that 
it  consists  of  an  exact  number  of  specks  of  electricity 
(electrons)  all  exactly  alike,  which  in  static  phe- 
nomena are  scattered  over  the  surface  of  the  charged 
body  and  hi  current  phenomena  are  drifting  along 
the  conductor." 


CHAPTER  IX 

ISOLATING  A  PROTON 

THAT  there  is  an  elemental  quantity  of  electricity 
was  definitely  shown  by  the  experiments  of  Millikan 
which  were  described  in  the  last  chapter.  His  ex- 
periments are  apparently  the  most  accurate  and  con- 
vincing because  of  their  simplicity.  They  constitute 
a  final  proof  in  a  long  series  of  independent  investi- 
gations by  various  physicists.  Some  had  experi- 
mented with  cathode  rays,  proved  that  they  were 
formed  by  small  charged  particles  and  found  the 
mass  and  charge  of  the  particles  (electrons) .  Others 
had  carried  out  similar  investigations  of  the  beta 
rays  from  radioactive  substances,  proved  their  gran- 
ular nature,  and  found  for  their  particles  the  same 
value  of  electrical  charge.  In  beta  rays,  however, 
the  electrons  move  with  high  velocities,  very  nearly 
that  of  light,  and  usually  much  higher  than  in 
cathode  rays.  The  investigators  found  that  while  the 
quantity  of  electricity  represented  by  an  electron  in 
a  beta  ray  was  the  same  as  that  in  a  cathode  ray,  the 
mass  was  in  general  much  greater,  that  it  depended 
upon  the  velocity  and  was  enormously  greater  for 
velocities  nearly  that  of  light.1 

The  quantity  of  electricity  which  constitutes  the 

1  Cf.  p.  205  of  the  Appendix. 

99 


100  WITHIN  THE  ATOM     • 

elemental  charge  had  also  been  determined  from  a 
knowledge  of  electrolytic  phenomena  and  by  deduc- 
tion from  certain  phenomena  of  radiation.  It  was 
determined  also  from  measurements  of  alpha  rays 
by  experimental  methods  similar  to  those  used  for 
cathode  rays.  In  the  case  of  gaseous  ions  the  ele- 
mental charge  had  been  determined  by  variations  of 
the  "cloud"  method  which  was  described  in  the 
preceding  chapter. 

The  net  result  of  all  these  experiments  has  been 
the  common  acceptance  of  the  idea  of  a  definite  ele- 
mental quantity  of  electricity,  and  its  identification 
with  the  electron  which  appears  in  cathode  rays  and 
beta  rays.  For  some  years,  however,  nothing  very 
definite  was  known  about  the  complement  of  the 
electron,  the  equivalent  positive  charge  of  electricity1 
which  we  are  calling  the  proton.  At  first  all  that 
could  be  said  was  that  an  atom  consisted  of  electrons 
which  could  be  isolated  and  a  nucleus  which  must 
have  a  positive  charge  equal  to  the  negative  charge 
represented  by  the  electrons  which  surrounded  it. 

Knowledge  of  the  elemental  positive  charge  has 
come  partly  from  a  study  of  radioactivity  and  partly 
from  a  study  of  conduction  through  gases.  The 
earlier  determinations  of  the  elemental  charge  by  the 
cloud  method  had  employed  the  ions  of  conducting 
gases,  sweeping  them  aside  from  their  normal  course 
by  highly  charged  plates  and  thus  collecting  similar 
ions  for  measurement.  Determinations  of  the  num- 
ber of  ions  in  these  experiments  were  based  upon 
the  phenomenon  discovered  by  C.  T.  R.  Wilson  that 

1  Which  is  usually  known  as  the  "positive  electron." 


ISOLATING  A  PROTON  101 

ions  act  as  centers  for  the  condensation  of  water 
vapor. 

This  phenomenon  Wilson  used  also  to  obtain  some 
interesting  pictures  of  the  progress  of  swiftly-moving 
charged  particles.  When  an  electron  is  shot  through 
a  gas,  in  which  there  is  a  large  amount  of  water 
vapor,  its  progress  is  recognizable  by  small  drops, 
formed  about  the  ions  which  result  from  its  collisions 
with  the  molecules  of  the  gas.  One  of  Wilson's  pic- 
tures of  the  path  of  a  high-speed  electron,  a  beta  par- 
ticle, is  reproduced  in  Fig.  12.  Drops  due  to  several 
ionizing  particles  are  seen  but  those  produced  by  the 
particular  particle  under  consideration  appear  as  a 
straight  line  lengthwise  through  the  center  of  the 
picture.  This  beta  particle  moved  so  rapidly  through 
the  atomic  systems  of  the  gas  and  the  free  spaces 
between  that  only  rarely  was  it  long  enough  in  the 
neighborhood  of  any  particular  electron  to  displace 
it  permanently  from  its  colleagues  in  an  atom.  It 
ionized  only  about  one  of  every  10,000  gas  molecules 
through  whose  systems  it  passed. 

In  Fig.  13,  on  the  other  hand,  appear  the  paths 
of  some  alpha  particles  from  radium.  Although 
these  heavier  particles  ionized  millions  of  gas  mole- 
cules in  each  centimeter  of  their  progress  they  were 
rarely  deflected  from  straight-line  paths.  In  two 
cases  in  this  figure  there  may  be  seen  sharp  changes 
in  their  directions.  These  occurred  near  the  ends 
of  their  paths,  when  their  energies  were  much  re- 
duced by  their  previous  activities,  and  are  believed 
to  represent  collisions  with  the  nuclei  of  gas  mole- 
cules. In  the  earlier  parts  of  their  paths  there  were 


102  WITHIN  THE  ATOM 

undoubtedly  some  similar  collisions  but  the  number 
was  relatively  small  and  the  momenta  of  the  alpha 
particles  were  such  that  they  suffered  inappreciable 
deflections.  Probably  they  drove  before  them  the 
molecules  of  gas  with  whose  nuclei  they  had  head-on 
collisions  much  as  does  the  cue  ball  in  a  well-played 
"follow  shot"  in  billiards.  The  smallness  of  the  alpha 
particle  and  of  the  nuclei  of  atoms,  in  general,  ex- 
plains, however,  the  infrequency  of  deflection  in 
those  later  portions  of  their  paths  when  their  abnor- 
mal energy  is  almost  entirely  absorbed  and  they  are 
becoming  as  the  other  atomic  systems  through  which 
they  pass. 

As  early  as  1911  Rutherford  applied  this  phe- 
nomenon, of  the  deflection  of  the  positive  alpha 
particle  by  the  positive  nucleus  of  an  atom,  to  a 
quantitative  determination  of  the  charge  on  the 
nucleus  of  various  types  of  atoms.  That  on  the  alpha 
particle  was,  of  course,  known  from  previous  work 
as  equal  in  amount  but  complementary  in  kind  to 
the  charge  of  two  electrons.  He  computed  the 
chance  that  an  alpha  particle  would  suffer  a  given 
deflection  by  being  shot  through  thin  sheets  of  foil 
of  gold  and  other  metals.  The  method  of  the  experi- 
ment involves  a  principle  which  is  widely  applied 
in  the  study  of  radioactivity. 

The  method  is  that  of  counting  scintillations. 
When  alpha  particles  strike  a  screen  of  zinc  sulphide, 
for  example,  they  give  rise  to  bright  specks  of  light. 
Each  particle  apparently  sets  into  vibration  the  elec- 
tronic systems  of  several  atoms  and  these  vibrations 
the  eye  recognizes  as  light.  The  phenomenon  is 


FIG.  12.  The  trails  of  beta  particles  (electrons),  moving  swiftly 
through  humid  air,  as  shown  by  drops  of  water  which  formed 
about  the  ions  produced  by  the  impacts  of  the  electrons.  (Re- 
produced from  original  memoir  of  C.  T.  R.  Wilson.) 


FIG.  13.  The  trails  of  alpha  particles  as  shown  by  the  con- 
densation of  water  vapor  on  the  ions  which  were  formed  by  their 
impacts.  (Original  in  scientific  memoir  of  C.  T.  R.  Wilson.) 


PLATE  I 


ISOLATING  A  PROTON  103 

similar  to  that  involved  in  the  recognition  of  the 
impact  of  cathode  rays  by  the  fluorescence  of  the 
glass  of  cathode  ray  tubes. 

The  particular  experiment  involved  finding  what 
fraction  of  a  thousand  alpha  particles,  which  were 
shot  through  a  sheet  of  foil,  produced  scintillations 
at  a  location  on  the  screen  corresponding  to  the  given 
angle  of  deflection.  It  was  determined  by  calcula- 
tion based  on  this  experimental  method  that  the 
number  of  elemental  charges  on  the  nucleus  of  an 
atom  is  approximately  equal  to  half  its  atomic 
weight. 

This  was  the  first  determination  of  atomic  num- 
bers. Although  the  method  is  not  capable  of  very 
exact  indications  and  although  the  values  obtained 
are  necessarily  only  indicative,  the  experiments  im- 
plied a  definite  granular  structure  to  positive  elec- 
tricity such  that  nuclei  of  different  atomic  systems 
differ  by  whole  numbers  of  elemental  positive 
charges.  It  gave  no  hope  of  isolating  the  elemental 
positive  charge  (proton). 

Further  indications  and  very  exact  quantitative 
results  on  atomic  numbers  were  obtained  about  three 
years  later  by  Moseley.  His  method,  however,  in- 
volved X-rays  and  will  be  discussed  in  the  following 
chapter. 

The  next  evidence  as  to  the  proton  came  from 
experiments  on  so-called  positive  rays.  In  the  con- 
duction of  electricity  through  gases,  as  we  have  seen, 
the  term  "cathode  rays"  was  applied  to  the  stream 
of  electrons  which  proceeds  away  from  the  negative 
electrode.  In  the  preceding  chapter  we  have  seen 


104 


WITHIN  THE  ATOM 


how  experimenters  arranged  a  hollow  anode  so  that 
a  pencil  of  these  rays  might  pass  beyond  the  anode 
and  be  subject  to  examination  or  use.  In  much  the 
same  way  the  term  "positive  rays"  has  been  applied 
to  the  positive  gaseous  ions  which  are  urged  toward 
the  cathode.  By  making  the  latter  a  hollow  cylinder 
these  positive  ions  may  be  passed  into  the  space 
beyond. 


FIG.  14 

Cross-section  of  apparatus  for  positive  ray  analysis.  (Illustrat- 
ing method  of  J.  J.  Thomson.)  The  stream  of  positive  ions  passed 
through  the  hollow  tubular  cathode,  C,  to  the  photographic  plate, 
P.  It  was  deflected  by  an  electric  field  (due  to  a  battery  con- 
nected at  +,  — )  and  by  an  electromagnet,  N-S,  and  thus  acted 
to  trace  a  parabolic  curve  on  the  plate.  Tube  L  connected  to  the 
vacuum  pump. 

If  the  cathode  is  a  long  cylinder  of  small  cross  sec- 
tion like  that  of  Fig.  14,  there  is  relatively  little 
diffusion  or  mixing  of  the  gases  of  the  two  parts  of 
the  vessel.  For  this  reason  the  gas  pressure  within 
the  conducting  portion  of  the  tube1  may  be  main- 


ISOLATING  A  PROTON  105 

tained  at  the  proper  value  to  secure  the  optimum 
density  of  gas  molecules  for  the  formation  of  ions 
and  the  remainder  of  the  enclosed  system  may  be 
practically  a  vacuum  and  thus  contain  few  mole- 
cules to  impede  the  progress  of  the  ions  which  con- 
stitute the  positive  rays.  At  the  end  of  this  second 
portion  of  the  tube  a  photographic  plate,  P,  permits 
a  record  of  the  stream,  for  each  ion,  as  it  strikes, 
disturbs  the  electronic  composition  of  the  neighbor- 
ing atoms  of  the  plate,  much  as  does  light  in  ordinary 
photography. 

In  one  sense,  of  course,  alpha  rays  are  positive 
rays.  They  are  helium  ions,  identical  with  helium 
atoms  which  have  lost  two  electrons  each.  They 
differ  from  helium  positive-rays,  which  would  be 
formed  if  the  tube  of  Fig.  14  contained  helium  in 
its  conducting  chamber,  in  their  origin,  for  alpha 
rays  arise  from  radioactive  disturbances.  They 
differ  also  in  velocity,  at  least  in  the  early  portion 
of  their  progress,  for  they  may  have  original  veloci- 
ties as  high  as  a  tenth  that  of  light.  In  conduction 
through  gases  no  such  high  velocities  are  attainable. 
They  may  differ  also  in  the  number  of  ions  which 
are  lost,  since  ionizing  impacts  in  a  conducting  gas 
usually  remove  only  a  single  electron  from  such 
stable  structures  as  the  inert  atoms,  although  they 
frequently  remove  two  from  substances  like  nitrogen, 
or  more  than  two  from  metallic  atoms  like  those  of 
mercury  vapor. 

It  was  this  high  velocity  and  hence  high  penetra- 
tion of  alpha  particles  which  permitted  Rutherford 
to  make  his  classical  demonstration  of  the  fact  that 


106 


WITHIN  THE  ATOM 


alpha  particles  are  really  helium  ions.  He  used  a 
very  thin-walled  tube  like  that  shown  at  A  in  Fig. 
15.  He  first  showed  that  there  was  no  connection 
between  A  and  the  larger  tube,  B,  by  filling  A  with 
helium  and  observing  that  there  was  none  of  the 
spectroscopic  characteristics  of  helium  gas  when  a 
current  passed  between  the  electrodes  of  C.  Next 


• 


FIG.  15 

Cross-section  of  Rutherford's  apparatus  for  showing  that  alpha 
particles  are  helium.  An  electric  current  through  C  gives  a 
radiation  characteristic  of  the  substance  in  B.  When  radium 
emanation  was  placed  in  A,  the  spectrum  of  the  radiation  from  C 
showed  traces  of  helium. 

he  removed  the  helium  from  A  and  substituted 
radium  emanation.  After  a  few  hours  the  spectro- 
scope showed  that  helium  was  present  in  the  dis- 
charge path  between  the  electrodes  of  C.  The  only 
way  helium  could  get  into  B  and  C  was  by  being 
identical  with  the  alpha  particles  which  are  emitted 
by  radium  emanation.  The  high  velocities  of  these 
particles  are  sufficient  to  carry  them  through  the 
atomic  systems  of  the  glass  walls  just  as  well  as 
through  less  closely  packed  atomic  systems  of  gases. 


ISOLATING  A  PROTON  107 

The  velocities  of  the  positive  ions  from  a  gas  which 
is  conducting  electricity  are  insufficient,  as  we  have 
said,  to  produce  some  of  the  effects  of  the  swift  alpha 
particles.  The  ions  do,  however,  affect  photographic 
plates  and  may,  therefore,  be  easily  studied.  Sup- 
pose, for  a  moment,  that  all  the  ions  which  form  the 
positive  rays,  from  such  a  tube  as  that  of  Fig.  14, 
are  of  the  same  mass.  They  will  differ  in  velocity 
because  they  have  been  formed  at  different  points 
in  the  tube,  have  fallen  through  different  potentials 


FIG.  16 
Parabolas  formed  on  the  plate,  P,  of  Figure  14. 

and  have  suffered  different  collisions.  Because  the 
beam  of  positive  rays  is  not  homogeneous  hi  velocity 
the  various  particles  which  compose  it  will  suffer 
different  deflections  under  the  influence  of  a  field  of 
force,  whether  magnetic  or  electrostatic. 

If  a  magnetic  system  is  so  placed  as  to  deflect  the 
particles  upward  some  of  them  will  be  deflected  but 
little,  others  more  and  the  result  will  be  a  line  of 
points  on  the  photographic  plate.  Such  a  line  is 
represented  as  ab  in  Fig.  16.  If,  now,  an  electro- 
static field  is  established  which  produces  a  deflection 
at  right  angles  to  that  of  the  magnetic  field,  each 


108  WITHIN  THE  ATOM 

component  particle  of  the. beam  will  be  deflected, 
say  to  the  right,  by  an  amount  which  depends  upon 
its  velocity.  The  result  is  a  series  of  spots  which 
lie,  as  shown  at  mn  of  the  figure,  on  a  portion  of  a 
parabola. 

For  positive  ions  of  some  different  mass  there  will 
be  formed  on  the  photographic  plate  a  different  para- 
bolic curve,  says  pq.  From  the  dimensions  of  these 
parabolas  there  may  be  calculated,  as  was  first  done 
by  J.  J.  Thomson,  the  ratio  of  the  masses  of  the 
types  of  particles  which  register  these  curves.  If 
the  tube  from  which  the  positive  rays  are  derived 
contains  a  mixture  of  gases  the  atomic  (or  molec- 
ular) weights  of  the  various  particles  may  be  de- 
rived from  the  various  traces  on  the  photographic 
plate.  If,  however,  the  particles  differ  not  only  in 
their  masses  but  also  in  the  charges  which  they 
acquire  by  ionization,  then  the  analysis  becomes 
more  complicated  or  even  impossible.  Two  par- 
ticles, one  having  twice  the  mass  of  the  other,  and 
carrying  twice  the  charge,  will  give  the  same  trace 
on  the  plate  for  the  method  separates  particles  only 
when  they  differ  in  their  ratios  of  mass  to  charge. 

In  one  of  Thomson's  experiments  he  studied  at- 
mospheric air,  which  contains  in  addition  to  nitrogen 
and  oxygen  small  amounts  of  inert  gases  like  neon 
and  argon.  From  the  tap-grease  which  was  used  to 
seal  the  valves  leading  to  the  vacuum  pump  there 
was  added  to  this  mixture  traces  of  carbon  dioxide 
and  carbon.  In  addition,  since  mercury  was  used  in 
the  pump,  there  was  a  trace  of  mercury  vapor.  In 
the  photograph  of  the  deflected  positive  rays  from 


FIG.  17.  Parabolas  obtained  in  positive  ray  analysis  by  J.  J. 
Thomson.  Neon  gave  two  parabolas.  A  and  B.  (A  retouched 
photograph  of  the  illustration  in  the  original  memoir.) 


FIG.  24.  Moseley's  photographs  of  the  X-ray  spectra  of  various 
metallic  anti-cathodes.  The  different  photographs  are  placed 
approximately  in  register  in  the  figure. 

PLATE  II 


ISOLATING  A  PROTON  109 

this  mixture  of  gases  and  vapors  Thomson  recog- 
nized molecules  of  nitrogen  and  carbon  dioxide  which 
had  lost  one  electron;  atoms  of  nitrogen,  oxygen, 
carbon,  neon,  and  argon  which  had  lost  one  electron 
each;  and  atoms  of  mercury  which  had  lost  re- 
spectively one,  two  and  three  electrons. 

The  appearance  of  the  curve  for  neon  was  much 
like  that  of  Fig.  17,  which  is  not  an  exact  copy  of 
the  original  photograph  but  was  retouched  to  ex- 
aggerate slightly  a  peculiarity  of  the  original. 
Apparently  there  are  two  curves,  A  and  B,  close  to- 
gether. From  the  more  prominent  curve,  A,  the  mass 
of  the  particle  was  found  to  be  20  and  from  the  other 
22.  In  this  way  the  isotope  of  neon  was  discovered. 

The  most  recent  and  reliable  series  of  analyses  of 
the  so-called  chemical  elements  by  the  method  of 
positive  rays  is  that  of  F.  W.  Aston.  He  discovered 
isotopes  of  other  chemical  substances,  like  chlorine, 
which  were  formerly  supposed  to  be  elementary.  In 
his  method  the  electrostatic  and  magnetic  fields  are 
arranged  so  that  their  deflections  occur  subsequent 
to  each  other  as  the  ray  progresses  instead  of  simul- 
taneously. The  precision  of  his  results  is  remarkable 
as  compared  to  other  positive  ray  analyses  for  the 
probable  error  of  his  determinations  is  only  about 
one-tenth  of  one  percent. 

Our  present  interest  in  his  work  is  due  to  the  fact 
that  he  not  only  isolated  the  proton,  that  is  the  posi- 
tive hydrogen  ion — for  Thomson  had  done  this  in 
his  analysis — but  he  made  for  its  mass  a  very  precise 
measurement.  Aston  compared  the  mass  of  the  pro- 


110  WITHIN  THE  ATOM 

ton  with  that  of  the  hydrogen  molecule  and  the  mass 
of  the  latter  with  that  of  the  helium  atom. 

You  will  remember  that  the  ordinary  chemical  de- 
terminations by  weighing  had  resulted  in  atomic 
weights  of  1.008  for  the  hydrogen  atom,  twice  as 
much  for  the  diatomic  hydrogen  molecule,  and  4.00 
for  the  helium  atom.  Aston's  determinations  are 
corroborative  and  indicate  definitely  that  the  mass 
of  the  proton,  when  free  or  when  constituting  the 
nucleus  of  a  hydrogen  atom,  is  eight-tenths  of  a  per- 
cent greater  than  when  it  is  combined  with  electrons 
in  a  nucleus. 

His  method  was  as  follows:  If  the  photographic 
plate  is  exposed  successively  to  impacts  of  ions  of  a 
given  mass  and  to  ions  of  twice  that  mass  which, 
however,  are  deflected  by  an  electrical  field  of  twice 
the  intensity,  then  the  two  traces  should  be  coinci- 
dent and  indistinguishable.  If,  on  the  other  hand, 
the  field  is  not  quite  doubled  the  line  for  the  atoms 
of  double  mass  will  lie  very  near  but  not  coincident 
with  that  for  the  atoms  of  single  mass.  Similarly  by 
taking  a  third  exposure  for  the  atoms  of  double  mass, 
but  using  for  deflection  an  electrostatic  field  as  much 
greater  as  it  had  formerly  been  less,  another  line  is 
obtained  equally  spaced  on  the  other  side  of  that 
recorded  by  the  atoms  of  single  mass. 

In  applying  this  method  he  exposed  a  plate  to 
positive  rays  containing  molecules  of  hydrogen  which 
had  been  ionized  by  the  loss  of  an  electron.  Then 
using  first  slightly  more  than  double  the  potential 
on  the  deflecting  plates  and  second  an  equal  amount 
less  than  this  double  potential,  he  obtained  two 


ISOLATING  A  PROTON  111 

records  for  helium  ions.  These  are  shown  in  Fig. 
ISA  which  is  a  drawing  based  on  the  photographs  of 
his  original  paper.  It  is  evident  that  the  trace  for 
the  hydrogen  molecule  is  not  midway  between  these 
bracketing  lines  as  it  would  be  if  the  mass  of  H2 
were  just  half  that  of  He.  On  the  other  hand  from 
Fig.  18s  it  is  seen  that  the  line  for  molecular  ions, 
H2,  is  equally  bracketed  by  the  lines  of  the  atomic 
ions,  Hj. 


i    M  I  II  n 


He  Ha       He  HI  H2  HI 

FIG.  ISA  FIG.  18u 

Drawing  based  on  the  positive  ray  photographs  by  means  of 
which  Aston  compared  the  atomic  weight  of  the  hydrogen  mole- 
cule with  that  of  the  helium  molecule  (Figure  A),  and  of  the 
hydrogen  atom  with  that  of  the  hydrogen  molecule  (Figure  B). 

Since  the  work  of  Aston  it  becomes  possible  to 
speak  definitely  of  an  element  of  positive  electricity, 
complementary  to  the  electron,  and  when  isolated 
equivalent  in  mass  to  the  hydrogen  atom.  When 
the  proton  is  not  isolated  it  is  apparently  secreted 
in  the  alpha  particles  which  are  known  constituents 
of  the  nuclei  of  the  radioactive  elements  and  by  in- 
ference constituents  of  all  others.  In  one  case,  that 
of  nitrogen,1  there  seems  to  be  direct  evidence  that 
the  proton  is  a  constituent  of  the  atomic  nucleus. 
The  evidence  was  obtained  during  1918  by  Ruther- 

1  In  a  letter  to  the  Editor  of  Nature,  March,  1921,  Rutherford 
announced  similar  phenomena  for  boron,  fluorine,  sodium, 
aluminum  and  phosphorus,  and  said,  "While  we  have  no  ex- 
perimental evidence  of  the  nature  of  these  particles,  except  in 
the  case  of  nitrogen,  it  seems  likely  that  the  particles  are  in 
reality  H  atoms." 


112  WITHIN  THE  ATOM 

ford  but  he  was  in  doubt  as  to  whether  it  indicated 
a  single  proton  or  a  particle  composed  of  two  such 
elements. 

The  isolated  positive  particles  of  which  he  ob- 
tained evidence  were  produced  from  nitrogen  by 
bombarding  its  molecules  with  alpha  particles.  As 
it  happens  alpha  particles  have  very  definite  ranges 
through  which  they  will  penetrate  before  losing  their 
ability  to  produce  scintillations.  For  each  radio- 
active substance  there  is  a  thickness  of  normal 
atmosphere  which  its  alpha  rays  can  penetrate.  For 
those  from  radium  the  range  is  3.5  centimeters  but 
for  radium  C  it  is  twice  as  much.  However,  if  the 
screen  whereby  scintillations  are  to  be  observed  is 
placed  more  than  seven  centimeters  from  radium  C 
there  are  still  occasional  scintillations.  These  have 
been  shown  to  be  due  to  ions  produced  and  driven 
forward  by  the  impacts  of  the  alpha  particles  with 
atoms  of  the  gas  through  which  they  pass.  For  ex- 
ample, if  the  atmosphere  is  hydrogen  scintillations 
are  observable  at  a  distance  from  the  source  effec- 
tively four  times  as  great. 

According  to  Rutherford  about  one  time  in  a  hun- 
dred thousand  an  alpha  particle  will  come  so  near 
to  hitting  the  nucleus  of  a  hydrogen  atom  as  to 
propel  it  along  the  line  of  its  own  motion.  His  cal- 
culations show  that  smaller  increases  in  range  should 
result  if  the  alpha  particles  are  projected  into  other 
gases  than  hydrogen;  thus  for  nitrogen  and  oxygen 
the  range  in  centimeters  should  be  extended  only 
from  7  to  7.8  and  9  respectively.  From  air,  there- 
fore, there  should  be  produced  a  few  long-range 


ISOLATING  A  PROTON  113 

particles  which  should  not  however  be  visible  beyond 
about  9  centimeters. 

He  found  that  the  actual  number  of  scintillations 
was  in  excess  of  that  expected  and  that  the  range 
w,as  practically  that  of  the  hydrogen  particles. 
When  pure  nitrogen  was  substituted  for  air  there  was 
an  increase  of  twenty-five  percent  in  the  number. 
Since,  by  volume,  air  is  four-fifths  nitrogen  we 
should  expect  the  effect  in  pure  nitrogen  to  be  five- 
fourths  as  large  if  it  were  solely  a  phenomenon  of 
nitrogen.  Rutherford  showed  conclusively  that  it 
was  such ;  but  he  was  unable,  with  the  small  number 
of  long-range  particles  which  were  formed  from  the 
nitrogen,  to  determine  whether  their  atomic  mass 
was  1  or  2.  As  he  said,  "From  the  results  so  far  ob- 
tained it  is  difficult  to  avoid  the  conclusion  that  the 
long-range  atoms  arising  from  collision  of  alpha  par- 
ticles with  nitrogen  atoms  are  not  nitrogen  atoms 
but  probably  atoms  of  hydrogen,  or  atoms  of  mass 
2.  If  this  be  the  case  we  must  conclude  that  the 
nitrogen  atom  is  disintegrated  under  the  intense 
forces  developed  in  a  close  collision  with  a  swift 
alpha  particle  and  that  the  hydrogen  atoms  which 
are  liberated  formed  a  constituent  part  of  the  nitro- 
gen nucleus." 

What  becomes  of  the  rest  of  the  nitrogen  nucleus? 
Nobody  knows.  The  determination  of  the  fact  of 
its  disintegration  was  an  experiment  requiring  a 
delicacy  of  operation,  an  imagination,  and  a  persist- 
ence of  which  only  a  master  is  capable.  If  he  failed 
to  detect  the  by-product  of  the  disintegration  it  must 
await  other  experiments  in  which  alpha  particles  of 


114  WITHIN  THE  ATOM 

greater  energy  shall  be  used  for  bombardment.  The 
guess  may  be  made,  however,  that  the  nitrogen  atom 
is  disrupted  into  two  long-range  particles  (protons), 
three  alpha  particles,  and  an  electron.1 

With  the  experiments  of  Thomson,  Aston,  Ruther- 
ford, and  others  we  may,  however,  take  as  definitely 
settled  a  granular  structure  for  positive  electricity 
and  an  atomic  nucleus  composed  of  these  grains  in 
close  combination  with  their  complementary  elec- 
trons. 

1  Rutherford,  apparently,  is  inclined  to  believe  that  nuclei  in- 
volve i particles  of  mass  3  and  charge  2  (that  is,  of  three  protons  and 
one  electron)  which  would  form  normal  atoms,  isotopic  with 
helium  (mass  4,  nuclear  charge  2).  In  this  connection  the  work 
of  W.  D.  Harkins  is  specially  important.  The  latter  has  shown 
that  for  all  known  atoms  (excepting  atoms  with  only  a  transitory 
existence,  such  as  those  produced  by  Rutherford)  the  atomic  mass 
and  atomic  number  can  be  explained  on  the  basis  of  a  nuclear 
structure  in  which  there  are  never  less  than  half  as  many  electrons 
as  protons.  For  atoms  of  even  atomic  number,  the  ratio  is 
exactly  %.  Such  atoms  as  analyses  have  shown  are  most  abundant 
in  meteorites  and  in  the  surface  of  the  earth.  They  are  apparently 
the  stable  atomic  forms.  Atoms  of  uneven  atomic  number  have 
slightly  higher  ratios  for  the  numbers  of  electrons  and  protons  in 
the  nucleus.  Rutherford's  nuclear  corpuscles  would  have  a  ratio 
of  1/3,  which  is  not  in  conformity  with  the  other  evidence.  Until 
further  evidence  is  presented  the  general  reader  may,  perhaps,  be 
safe  in  assuming  atomic  structures  to  be  composed  of  alpha 
particles  and  in  some  cases  to  include  extra  protons. 


CHAPTER  X 

X-RAYS  AND  ATOMIC  NUMBERS 

EXPERIMENTS  on  the  scattering  of  alpha  rays  by 
their  collisions  with  the  nuclei  of  atoms  in  passing 
through  thin  sheets  of  metal  early  indicated  an  ap- 
proximate relationship  of  nuclear  charge  to  atomic 
weight  of  one  to  two.  The  exact  determination, 
however,  of  the  excess  of  protons  in  the  nucleus  of 
each  type  of  atomic  system  was  the  result  of  work 
by  Moseley  and  others  who  applied  and  extended 
his  methods.  To  understand  the  experiments  we 
must  consider  X-ray  phenomena  and  the  construc- 
tion of  crystals. 

X-rays,  or  Roentgen  rays  as  they  were  once  called 
after  their  discoverer,  arise  from  the  impacts  of  a 
stream  of  swiftly  moving  electrons  with  ordinary 
matter,  as,  for  example,  with  a  plate  of  platinum. 
From  the  atoms  which  are  struck  by  the  electrons 
there  proceeds  a  radiation  which  we  now  know  to 
be  identical  with  visible  light  except  for  the  fre- 
quencies which  are  involved. 

Heat  rays,  light,  ultra-violet  rays,  X-rays,  the 
gamma  rays  which  have  been  mentioned  as  some- 
times accompanying  electron  streams  from  radio- 
active substances,  and  the  Hertzian  rays  used  in 
radio-communication  are  all  radiations  of  the  same 

115 


116  WITHIN  THE  ATOM 

character  except  for  differences  in  the  frequency  of 
the  vibrations  from  which  they  originate.  Except 
for  heat  rays,  which  are  believed  to  be  due  to  mo- 
tions of  atomic  systems,  and  except  for  Hertzian 
waves  which  are  due  to  the  surges  back  and  forth  of 
electrons  in  wire  systems  which  are  conducting  alter- 
nating currents,  all  other  radiations  are  due  to 
vibrations  of  the  electrical  elements  within  atomic 
systems. 

Vibration  and  oscillation  are  synonymous  terms. 
Both  imply  that  a  body  moves  back  and  forth 
through  an  equilibrium  position.  The  farther  it 
moves  from  this  position  the  greater  is  its  tendency 
to  return.  A  simple  case  of  oscillation  is  that  of  the 
pendulum  bob  of  a  clock.  We  start  it  by  swinging 
it  aside  from  its  equilibrium  position  and  thus  lifting 
it  further  from  the  earth.  The  tractation  of  earth 
and  bob  then  results  in  a  motion  of  the  bob  toward 
its  unstressed  position.  As  it  swings  back  it  moves 
faster  and  faster.  When  it  reaches  the  bottom  of  its 
swing  it  has  an  energy  (kinetic)  which  is  equal  to 
that  contributed  in  raising  it,  except,  of  course,  for 
subtractions  by  friction  with  the  air.  By  virtue  of 
this  kinetic  energy  it  continues  in  motion.  It  can 
rise,  however,  only  to  the  height  of  its  original  sepa- 
ration in  the  opposition  direction.  At  any  greater 
height  it  would  have  greater  potentialities  of  energy. 
It  rises,  therefore,  until  the  kinetic  energy  which  is 
associated  with  it  in  the  equilibrium  position  is  con- 
verted into  potential  energy.  At  this  point  it  pauses 
and  reverses  it?  motion.  The  time  required  for  one 
complete  trip,  that  is  the  interval  between  two  sue- 


X-RAYS  AND  ATOMIC  NUMBERS 


117 


cessive  motions  in  the  same  direction  through  the 
same  point  of  its  path,  is  called  the  period  of  its 
oscillation.  The  number  of  periods  per  second  is  the 
frequency. 

Oscillations  in  general  are  not  restricted   to   a 


FIG.  19 
Illustrating  oscillations  due  to  three  restoring  forces. 

linear  path  as  in  this  simple  case  where  there  is  but 
a  single  restoring  force,  namely  that  of  gravitation. 
Suppose,  for  example,  that  a  body  is  constrained  by 
forces  which  have  components  at  right  angles  in  the 
three  directions  represented  by  the  springs  of  Fig.  19. 
If  it  is  displaced  from  its  equilibrium  point  in  the 


118  WITHIN  THE  ATOM 

direction  of  the  arrow  all  three  forces  will  be  active 
in  its  restoration  and  it  will  execute  the  most  general 
type  of  vibration.  Its  frequency,  which  is  still  de- 
fined as  above,  depends  upon  the  inertia  of  the  body 
and  the  nature  of  the  restoring  forces. 

In  the  case  of  molar  bodies,  like  the  pendulum  of 
the  preceding  illustration,  there  is  always  a  gradual 
dissipation  of  energy  from  the  vibrating  system  to 
surrounding  systems.  Energy  is  given  to  the  adja- 
cent molecules  of  the  air  and  by  them  passed  on  to 
more  distant  molecules.  If  the  frequency  of  a  vibrat- 
ing mechanical  system  is  within  a  certain  range  the 
vibratory  motions  of  the  air  molecules  may  set  up 
vibrations  within  the  human  ear  which  are  recog- 
nized as  sound  of  a  definite  pitch  or  vibration-fre- 
quency. Above  20,000  vibrations  per  second,  how- 
ever, the  vibrations  are  usually  inaudible  for  the 
human  ear  is  but  little  sensitive  outside  the  impor- 
tant frequency  range  of  the  human  voice  which  ex- 
tends from  about  200  to  about  5000. 

Between  the  vibrations  of  molar  bodies,  which  are 
observed  as  sound,  and  those  of  electrons  within 
atomic  structures,  which  are  observed  as  light,  there 
are  several  important  differences.  In  one  case  the 
vibrating  systems  are  aggregates  of  molecules  and 
in  the  other  discrete  electrons.  The  restoring  forces 
are  usually  due  to  elasticity  in  the  case  of  sources 
of  sound,  and  hence  to  intermolecular  forces,  but 
for  light  they  are  intra-atomic.  The  medium  by 
which  energy  is  transmitted  from  the  vibrating 
source  is  molecular  in  one  case;  in  the  other  it  is  at 
best  a  mere  postulate,  as  to  which  more  shall  be 


X-RAYS  AND  ATOMIC  NUMBERS         119 

said  later.  The  frequencies  involved  in  sound  are 
expressed  in  hundreds  or  thousands,  while  those  for 
light  are  expressed  in  millions  of  millions,  extending 
from  375  million  million  at  the  red  end  of  the  visible 
spectrum  to  750  million  million  at  the  violet  end. 

The  difference,  however,  which  is  most  incompre- 
hensible is  that  involved  in  the  phenomena  of  ab- 
sorption and  emission  of  energy.  When  a  violin  string 
is  set  into  vibration  the  energy  with  which  it  starts 
depends  upon  what  energy  was  contributed  to  it  hi 
producing  its  initial  displacement.  As  the  string  is 
continuously  displaced  there  is  added  continuously 
the  energy  with  which  it  shall  engage  in  vibration. 
In  its  subsequent  vibration  this  energy  is  continu- 
ously dissipated  in  truly  infinitesimal  amounts  to 
the  surrounding  molecules.  Both  the  absorption  and 
the  emission  of  energy  are  conceived  as  continuous 
phenomena,  just  as  if  there  was  a  flow  of  a  fluid 
energy  which  is  infinitely  divisible. 

There  is  no  such  phenomenon  as  occurs  in  our 
money  economy  where  human  energy  is  conceived 
to  be  expended  in  quantities  adequately  represented 
by  monetary  units.  Our  stored  energy  grows  by 
dollars  or  by  pennies  but  the  energy  of  the  system 
we  are  considering  increases  or  decreases  continu- 
ously by  amounts  which  are  infinitely  small  parts  of 
any  of  our  usual  units  for  energy. 

In  the  case  of  electronic  oscillators,  on  the  other 
hand,  there  is  evidence  that  they  emit  energy  only 
in  definite  quantities  the  values  of  which  depend 
upon  the  frequencies  of  their  oscillations.  Whether 
or  not  the  operation  of  absorbing  energy  also  takes 


120  WITHIN  THE  ATOM 

place  discontinuously  by  similar  units  is  still  de- 
batable and  awaits  further  evidence.  It  may  be  that 
the  electronic  systems  can  absorb  continuously  in 
infinitesimal  amounts  but  can  emit  only  discon- 
tinuously in  definite  "quanta,"  just  as  warlike  na- 
tions may  tax  the  tiny  energies  of  their  citizens  to 
expend  in  dreadnoughts. 

Unlike  the  vibrating  systems  of  mechanics, 
whether  actual  or  theoretical,  the  vibrating  systems 
of  the  electrons  within  an  atom  do  not  radiate 
energy  continuously  but  emit  it  in  definite  quanta. 
According  to  the  present  accepted  picture  the  elec- 
trons may  vibrate  in  orbits  without  loss  of  energy  to 
surrounding  systems.  (This  in  itself  is  an  argument 
against  an  all-embracing  ethereal  medium,  for  if  it 
was  capable  of  absorbing  energy  at  all  from  a  vibrat- 
ing electron  we  should  expect  it  to  do  so  continu- 
ously.) When,  however,  there  is  a  change  in  the 
orbital  motion  of  an  electron,  then  a  quantum  of 
energy  is  shot  out.  This  quantum  travels  with  the 
enormous  velocity  of  30,000  million  centimeters  a 
second,  that  is  with  the  velocity  of  light. 

The  quantum  itself  is  not  a  unit  of  energy  but 
rather  a  specific  amount.  It  is  specific  for  any  given 
frequency  of  vibration  and  in  terms  of  the  ordinary 
unit  of  energy  is  numerically  equal  to  the  product 
of  the  frequency  by  a  fixed  number,  known  from 
the  originator  of  the  "quantum  theory"  as  "Planck's 
constant." 

For  any  type  of  atomic  system  there  appears  to 
be  a  fairly  large  number,  for  example  nearer  to  a 
hundred  than  to  ten,  of  possible  orbits  for  the  planet- 


X-RAYS  AND  ATOMIC  NUMBERS         121 

ary  electrons.  Radiation  occurs  when  an  electron 
passes  from  a  less  stable  to  a  more  stable  orbit.  By 
interactions  with  other  atomic  systems,  if  they  are 
in  violent  motion,  or  with  swiftly  moving  electrons, 
a  planetary  electron  may  be  displaced  into  a  less 
stable  orbit.  During  its  return  energy  is  radiated. 

Violent  interactions  give  rise  to  higher  frequencies 
than  do  those  which  can  contribute  less  energy.  The 
gamma  rays  from  radioactive  substances  and  the 
X-rays  which  arise  from  impacts  of  swiftly  moving 
electrons  with  atomic  systems  have  the  highest  fre- 
quencies so  far  observed. 

As  to  their  relations  of  energy  and  frequencies 
more  will  be  said  later  after  considering  the  physical 
means  for  the  production  of  X-rays.  The  latter  may 
always  be  produced  when  a  stream  of  electrons  im- 
pinges on  a  plate,  provided  that  the  individual  elec- 
trons have  sufficient  kinetic  energy.  In  the  original 
X-ray  tube  the  electrons  were  obtained  in  the  form 
of  a  cathode  stream  which  arose  from  the  cathode 
as  the  result  of  its  bombardment  by  positive  ions. 
The  modern  X-ray  tube  avoids  the  difficulty  of  con- 
trol which  is  inherent  in  the  use  of  a  gaseous 
conductor  and  obtains  the  cathode  stream  by  thermi- 
on ically  emitting  electrons  in  a  manner  similar  to 
that  described  for  another  vacuum  tube  device  in 
Chapter  VII. 

The  Coolidge  X-ray  tube,  in  which  this  principle 
is  applied,  is  shown  in  Fig.  20.  A  spiral  tungsten 
wire,  C,  serves  as  the  cathode  and  is  heated  by  pass- 
ing through  it  a  current  from  a  battery.  The  anode, 
A,  is  a  massive  block  of  tungsten.  The  anode  is 


122 


WITHIN  THE  ATOM 


maintained  positive  with  respect  to  the  cathode  by 
a  source  of  very  high  potential.  There  is  thus  drawn 
across  the  intervening  vacuum  a  stream  of  swiftly 
moving  electrons  which  are  further  encouraged  to 
focus  upon  the  anode  by  enclosing  the  cathode  in  a 
tube  of  molybdenum,  shown  in  cross  section  at  M. 


FIG.  20 

Cross-section  of  Coolidge  X-ray  tube.  Electrons,  thermionically 
emitted  from  the  cathode,  C,  are  drawn  across  the  highly  evacu- 
ated space  to  the  anti-cathode,  A,  from  which  X-rays  arise.  High 
voltage  is  applied  between  +  and  — . 

The  electrons  of  this  stream  violently  displace 
from  their  orbits  some  of  the  electrons  of  the  atoms 
upon  which  they  fall.  The  bombardment  appar- 
ently affects  not  only  electrons  more  or  less  loosely 
held  in  the  outer  shells  of  the  atoms — those  which 
account  for  valence  and  ionization — but  affects  also 
electrons  in  the  inner  shells.  These  are  displaced  to 
new  orbits  from  which  they  return  to  their  original 
ones.  The  return  is  accompanied  by  an  emission 


X-RAYS  AND  ATOMIC  NUMBERS         123 

of  energy.  Because  these  inner  electrons  are  closely 
bound  by  the  nucleus  the  restoring  forces  are  large 
and  the  frequencies  high,  in  much  the  same  way  that 
tightening  a  violin  string  increases  the  pitch  of  the 
note. 

For  X-rays  the  frequency  may  be  twenty  thousand 
times  that  of  visible  light,  which  is  apparently  pro- 
duced by  electrons  further  from  the  nucleus.  On 
the  other  hand,  even  higher  frequencies  are  obtained 
when  the  displacement  of  an  electron  is  caused  by 
the  ejection  of  a  beta  particle  from  the  nucleus  it- 
self. For  gamma  rays  which  arise  in  this  way  the 
frequencies  are  ten  to  a  hundred  times  as  high  as  for 
X-rays. 

The  emission  and  absorption  of  X-rays  are  com- 
plementary phenomena.  As  just  stated,  their  emis- 
sion results  from  the  displacement  of  electrons  by 
foreign  electrons  which  violently  intrude  into  the 
inner  circles  of  the  atom.  When,  in  turn,  these 
X-rays  impinge  upon  atoms  they  eject  electrons  and 
disturb  the  quiet  orbital  motions  of  the  inner  circles. 
Two  different  phenomena  are,  therefore,  involved 
when  a  body  is  exposed  to  X-rays,  first,  the  ioniza- 
tion  of  some  of  its  atoms,  a  phenomenon  which  will 
be  discussed  later  in  connection  with  other  cases  of 
ionization  by  radiant  energy,  and,  second,  the  pro- 
duction of  orbital  changes  which  are  of  the  same 
general  character  as  those  occurring  in  the  atoms  of 
the  anode  from  which  the  rays  arose. 

The  second  phenomenon  is  one  of  re-radiation. 
The  electrons  of  atoms  which  are  exposed  to  X-rays 
are  displaced  from  their  normal  orbits  and  in  their 


124  WITHIN  THE  ATOM 

return  they  radiate  energy.  The  X-rays  which  arise 
from  a  body  exposed  to  X-rays  are  so-called  second- 
ary X-rays.  The  re-radiation  may  involve  X-rays 
different  from  those  incident  upon  the  body.  Some 
of  the  re-radiation  will  be  of  the  same  character  as 
the  original  X-rays  which  are  then  said  to  be  "scat- 
tered" by  the  body. 

The  last  term  is  well  chosen,  since  orderly  reflec- 
tion, to  which  we  are  accustomed  in  the  case  of 
polished  mirrors  and  light  rays,  does  not  occur.  Such 
reflection  is  possible  only  if  the  surface  irregularities 
of  the  reflecting  body  are  negligible  in  comparison 
to  "the  wave  length,"  so-called,  of  the  incident  radia- 
tion. By  wave  length  is  meant  the  distance  which 
radiant  energy  travels  during  each  period  of  the 
vibrating  source.  For  X-rays  this  distance  is  just 
about  half  the  diameter  of  an  ordinary  diatomic 
molecule.  No  surface,  therefore,  can  be  smooth  to 
X-rays  and  reflecting  in  the  ordinary  sense.  For 
this  reason  the  re-radiation  of  X-rays  is  usually 
irregular  and  disorderly. 

It  was  pointed  out,  however,  by  Laue  in  1912  that 
X-rays  would  be  reflected  in  an  orderly  manner  by 
the  regularly  spaced  molecules  of  crystals,  and  fur- 
ther that  by  this  means  the  wave  length  of  various 
X-rays  could  be  determined,  provided  that  the  dis- 
tances between  the  molecules  of  the  crystal  were 
known.  The  experimental  method  was  perfected 
shortly  after  by  W.  L.  and  W.  H.  Bragg. 

The  principle  involved  may  be  explained  by  the 
following  analogy:  Imagine  the  points  in  Fig.  21 
to  represent  widely  separated  gymnasts  who  are  to 


X-RAYS  AND  ATOMIC  NUMBERS         125 

perform  identical  sequences  of  motions  at  the  orders 
or  counts  of  a  distant  captain,  C.  Because  the  energy 
vocally  emitted  by  the  captain  takes  a  finite  time  to 
travel  to  the  gymnasts  each  receives  the  order  an 
instant  later  than  his  next  neighbor  who  is  nearer 
the  source.  Therefore,  they  do  not  perform  in  step. 
Suppose  that  each  gymnast  counts  aloud  as  he 
executes  the  characteristic  motions.  There  will  be 
some  point,  as  X,  where  an  auditor  would  hear  the 
counting  of  all  as  if  they  were  actually  counting  in 
unison.  This  point  must  be  so  located  that  the  time 


b 

FIG.  21 

Diagram  to  show  the  principles  involved  in  the  spectral  analysis 
of  X-rays  by  a  crystal  grating. 

required  for  the  sound  to  travel  over  the  path  aX 
is  greater  than  that  for  the  path  bX  by  just  the 
amount  of  time  which  gymnast  b  is  behind  gymnast 
a  in  his  counting.  On  either  side  of  X  the  auditor 
will  receive  a  jumble  of  unintelligible  and  interfering 
sounds.  At  X,  however,  the  sounds  reenforce  each 
other.  If  the  gymnasts  are  mechanically  perfect  in 
their  tasks  and  in  their  rhythm  the  point  X  will  be 
sharply  defined  by  absolute  silence  on  either  side, 
of  it.  Such  precision  is  attainable  in  the  case  of 
electronic  gymnasts. 

There  will  be  other  points  also,  like  X'  and  X" ', 


126  WITHIN  THE  ATOM 

where  there  will  be  similar  sharp  maxima  of  re- 
radiated  energy.  The  first  of  these  will  be  the  point 
where  the  counts  heard  from  a  are  one  whole  series 
behind  those  of  b.  Under  these  conditions  the  dis- 
tance aX'  is  a  whole  wave  length  greater  than  the 
distance  bX'. 

The  actual  location  of  these  points  depends  upon 
the  wave  length  of  the  radiant  energy  and  upon  the 


FIG.  22 


Representation  of  a  cubic  crystal.  If  the  crystal  is  that  of 
common  salt,  sodium  atoms  are  as  represented  by  black  circles 
and  the  chlorine  atoms  by  light  circles. 

spacing  of  the  re-radiating  centers.  If  the  latter  is 
known  the  wave  length  may  be  determined.  Now 
in  crystals  of  certain  types,  namely  cubic,  only  cer- 
tain relatively  simple  arrangements  of  the  molecules 
are  possible.  For  example,  Fig.  22  shows  the  simple 
arrangement  for  NaCl  and  similar  substances.  The 
molecules,  however,  are  diatomic  and  the  crystal 
structure  is  built  primarily  with  reference  to  the 


X-RAYS  AND  ATOMIC  NUMBERS         127 

atoms,  as  we  would  expect  from  our  knowledge  of 
the  opposite  valence  of  sodium  and  chlorine.  Adja- 
cent to  each  atom  of  sodium  is  one  of  chlorine.  The 
black  circles  in  the  diagram  represent  the  sodium 
atoms  and  the  other  circles  the  chlorine  atoms. 

Each  atom  of  each  kind  must  be  shared  by  eight 
small  contiguous  cubes,  which  are  indicated  by 
dotted  lines.  However,  each  small  cube  has  asso- 
ciated with  it  four  atoms  of  each  kind.  We  are, 
therefore,  correct  in  assigning  to  each  small  cube 
of  a  rock-salt  crystal  four-eighths  of  the  mass  of  each 
kind  of  atom.  From  a  knowledge  of  the  mass  of 
each  type  of  atom  and  from  the  measured  mass  and 
volume  of  such  crystals  very  accurate  data  are  made 
available  as  to  the  dimensions  of  these  small  cubes. 

Measurements  of  the  tiny  wave  lengths  involved 
in  X-rays  are,  therefore,  made  possible  by  the  use 
of  crystals  for  which  the  dimensions  of  the  "lattices" 
are  known.  The  frequencies  corresponding  are  then 
obtainable  by  simple  arithmetic. 

In  such  measurements  the  crystal  is  merely  a  por- 
tion of  the  instrument  and  there  is  no  further  con- 
cern with  the  physical  mechanism  whereby  it 
operates.  Such  was  the  use  to  which  Moseley  put 
crystals  in  his  famous  investigations  of  1914  before 
his  life  was  sacrificed  to  a  World  War.  He  used  the 
crystal  grating  which  we  have  described  above  for 
the  determination  of  the  characteristic  X-ray  fre- 
quencies of  various  substances.  The  oscillators  of 
the  crystal  will  respond  to  radiations  of  a  wide  range 
of  X-ray  frequencies  and  re-radiate  the  same  fre- 
quency as  that  with  which  they  are  excited. 


128 


WITHIN  THE  ATOM 


Substances,  however,  which  give  rise  to  primary 
X-rays,  instead  of  secondary,  that  is  those  which  are 
bombarded  by  electrons,  emit  rays  which  have  fre- 
quencies characteristic  of  their  atomic  structure. 
Each  type  of  atom  emits  a  characteristic  group  of 
X-rays.  For  example,  when  silver  is  used  as  the  anti- 
cathode  of  an  X-ray  tube  the  point  X'  of  Fig.  21 
appears  not  as  a  single  point  but  as  two  near-by 
points,  for  two  slightly  different  frequencies  of  X- 
rays  are  simultaneously  emitted. 


FIG.  23 

Cross-section  of  an  X-ray  spectrometer.  X-rays  from  the  anti- 
cathode,  F,  pass  to  a  crystal  grating,  C.  The  spectrum  there 
formed  is  detected  by  a  photographic  plate,  mounted  beyond  the 
screen,  D. 

In  the  examination  of  X-rays  by  means  of  a 
crystal,  instead  of  using  a  point  source  as  in  Fig.  21, 
a  narrow  line  source  is  used.  To  obtain  such  a  source 
the  X-rays  from  the  tube  are  cut  off  by  lead  plates 
in  which  there  are  slits,  shown  in  cross  section  at 
A  and  B  in  Fig.  23.  A  narrow  rectangular  beam  is 
thus  allowed  to  fall  on  the  crystal  C  of  this  figure. 
The  crystal  may  be  rotated,  as  may  also  the  tube 
marked  D.  The  re-radiated  beam  traverses  this  tube, 


X-RAYS  AND  ATOMIC  NUMBERS          129 

passes  through  another  slit  in  a  lead  plate  and  falls 
upon  a  photographic  plate. 

Moseley  took  photographs  successively  of  the 
X-radiation  from  various  types  of  anti-cathodes. 
Some  of  these  are  reproduced  in  Fig.  24  (Plate  II, 
opposite  p.  108). 

A  series  of  similar  photographs  taken  by  Siegbahn 
are  reproduced  in  Fig.  25.  (Plate  III.)  Consider 
the  left-hand  series.  As  the  substance  from  which 
the  rays  are  emitted  is  changed  from  arsenic  (As)  to 
selenium  (Se),  or  from  rubidium  (Rb)  to  strontium 
(Sr),  there  occurs  the  same  shift  in  the  spectrum 
which  is  of  common  characteristic  form  for  all  the 
elements. 

This  particular  spectrum  is  that  of  the  K  type  of 
X-rays.  Of  the  different  types  more  will  be  said 
later.  For  the  present  it  may  be  noted  that  they 
differ  in  their  origin,  and  that  the  K  type  is  excited 
only  by  more  swiftly  moving  electrons  than  will  give 
rise  to  the  L  type.  Characteristic  spectra  of  the  L 
type  are  shown  on  the  right-hand  side  of  Fig.  25. 

For  both  types  there  was  found  a  simple  relation- 
ship between  the  frequencies  of  the  characteristic 
radiations  of  a  large  number  of  elements.  The  fre- 
quencies progressed  according  to  a  simple  rule  as 
successive  elements  in  the  periodic  table  were  ex- 
amined. When  the  elements  were  arranged  in  order 
of  their  characteristic  frequencies  it  was  found  that 
each  was  obtainable  from  its  predecessor  by  simple 
addition.  Apparently  each  element  of  the  periodic 
series  differs  from  the  next  lower  by  the  addition  of 
a  definite  amount  of  electricity  which  is  accom- 


130  WITHIN  THE  ATOM 

panied  by  an  increase  in  frequency  of  the  charac- 
teristic radiation.  It  is  the  nuclear  charge  which 
increases  and  thus  gives  rise  to  greater  restoring 
forces  and  more  rapid  vibrations  when  the  inner 
electrons  are  displaced. 

Moseley's  discovery  of  a  simple  numerical  rela- 
tionship between  characteristic  frequencies  did  not 
involve  measurements  on  all  the  known  elements. 
Below  sodium,  for  example,  there  are  ten  elements 
for  which  no  X-ray  spectra  have  yet  been  obtained. 
The  inert  elements  also  must  of  necessity  be  omitted. 
Thus  you  will  notice  that  krypton  (atomic  number 
36)  is  omitted  in  Fig.  25.  His  work  and  conclusions, 
however,  have  been  corroborated  by  many  other 
tests  and  may  be  considered  the  first  definite  proof 
of  the  structure  of  the  atomic  nucleus  by  grains  of 
positive  electricity  (protons). 

Part  of  the  corroboration  has  come  from  measure- 
ments on  the  characteristic  absorption  which  ele- 
ments show  for  X-rays.  This  work  was  done  in  1916 
by  DeBroglie  although  the  discovery  of  such  absorp- 
tion dates  from  Barkla's  work  in  1909. 

In  an  X-ray  beam  there  is  present,  in  addition  to 
the  characteristic  frequencies  which  arise  from  the 
vibrations  of  electrons  within  the  atoms  of  the  anti- 
cathode,  more  or  less  radiation  of  other  frequencies 
below  those  which  are  characteristic.  A  haphazard 
jumble  of  disturbances  of  all  degrees  of  suddenness 
accompanies  the  impacts  of  the  various  electrons  of 
a  cathode  stream.  These  are  analysed  by  the  crystal 
spectrometer  into  a  consecutive  series  of  recurring 
disturbances  which  then  have  the  appearance  of 


*=•  a  o 

3~-§ 


3 


OD 


Q 


i2  «d 

o3    j 


5  1^ 

K 


3  as 


bC  o 


X-RAYS  AND  ATOMIC  NUMBERS         131 

radiations  of  definite  frequencies.  A  continuous 
spectrum  is  thus  formed.  The  appearance,  however, 
is  due  entirely  to  the  regularity  of  structure  of  the 
crystal  or  other  instrument  of  analysis  and  is  not 
inherent  in  the  X-rays  themselves. 

The  amount  of  this  general  or  so-called  "white" 
radiation  is  relatively  small  and  does  not  obscure 
the  more  pronounced  characteristic  radiation.  At 
the  top  of  Fig.  26,  for  example,  there  appears  a 
photograph  of  the  X-radiation  from  tungsten  as 
taken  through  a  crystal  spectrometer,  like  that  of 
Fig.  23,  except  that  the  slit  D  is  omitted  so  that  a 
wide  range  of  frequencies  may  reach  the  plate.  In 
addition  to  the  continuous  spectrum  of  X-rays  two 
series  of  characteristic  lines  are  visible,  namely,  the 
K  series  near  the  central  black  band,  and  the  L  series 
further  to  the  right. 

The  central  black  image  corresponds  to  X  of  Fig. 
21.  Each  of  the  other  lines  corresponds  to  X'  of  this 
figure  for  there  is  a  different  location  of  X'  for  each 
frequency  involved  in  the  beam  of  X-rays.  The 
separation  of  X  and  each  X'  is  greater *  the  smaller 
the  frequency  of  the  vibratory  motion  which  the 
crystal  spectrometer  is  detecting.  For  tungsten  with 
its  high  atomic  number  of  74  the  K  lines  are  due 
to  radiations  of  correspondingly  high  frequency  and 
are  very  close  to  the  central  image.  The  L  series 

1  In  the  photographs  of  Fig.  25  the  central  image  corresponding 
to  X  appears  at  the  extreme  left.  From  these,  it  is  seen  that  the 
higher  the  frequency,  that  is  the  higher  the  atomic  number,  the 
closer  to  the  central  image  will  be  the  spectral  line  corresponding 
to  X'. 


132  WITHIN  THE  ATOM 

which  have  about  one-seventh  the  frequencies  of 
the  K  lines  are  well  separated  from  the  center. 

The  second  photograph  of  Fig.  26  was  made  by 
inserting  in  the  path  of  the  X-rays  from  tungsten  a 
thin  sheet  of  molybdenum.  The  K  lines  are  no 
longer  visible.  In  fact,  above  a  definite  frequency  all 
the  radiation  from  the  tungsten  has  been  absorbed 
and  for  a  certain  region  to  the  right  of  the  central 
image,  the  photographic  plate  has  been  unaffected. 
If  antimony,  of  atomic  number  51,  replaces 
molybdenum,  of  atomic  number  42,  the  absorption 
band  does  not  extend  to  as  low  frequencies.  In  gen- 
eral it  has  been  found  that  the  limiting  frequencies 
at  which  absorption  begins  are  sharply  marked,  are 
characteristic  of  the  atom  of  the  absorbing  material, 
and  increase  with  the  atomic  number. 

Before  carrying  the  discussion  further  an  explana- 
tion must  be  given  for  two  edges  of  light  and  dark 
which  occur  in  the  first  photograph  of  Fig.  26.  These 
are  marked  Ag  K«  and  Br  K«.  They  are  the 
boundaries  of  absorption  for  silver  and  bromine. 
They  were  obtained  by  inserting  a  thin  film  in- 
volving atoms  of  these  substances.  X-ray  absorp- 
tion is  a  function  of  the  electrons  within  an  atom  and 
hence  without  prejudice  an  atom  may  be  a  partner 
in  any  sort  of  molecular  union.  In  this  particular 
case  the  film  of  silver  bromide,  AgBr,  was  the  sensi- 
tized film  of  the  photographic  plate  itself. 

An  element  will  absorb  radiation  of  frequency 
higher  than  that  of  its  own  characteristic  X-ray 
radiation.  If,  therefore,  a  given  radiation  is  im- 
pressed successively  upon  the  elements  of  the 


w 

Kj8    Ka 


Absorption  in  Molybdenum  (42) 


I 


Absorption  in  Cadmium  (48) 


Absorption  in  Antimony  (51) 


FIG.  26.  X-ray  absorption  spectra.  The  upper  photograph 
shows  X-rays  from  a  tungsten  anti-cathode.  The  lower  photo- 
graphs show  absorption  of  this  radiation  by  plates  of  molybdenum, 
cadmium  and  antimony.  (Reproduced  from  memoir  of  DeBroglie.) 


FIG.  28.  The  path  of  an  X-ray  through  humid  atmosphere.  It 
is  marked  by  the  ionization  trails  of  the  electrons  which  it  ejects 
from  the  gas  molecules.  (Reproduced  from  memoir  of  C.  T.  R. 
Wilson.) 


FIG.  31.  A  line  spectrum  of  hydrogen.  The  hydrogen  spectrum 
is  bracketed  by  an  iron  spectrum  which  furnishes  a  comparison 
scale.  (A  section  of  photograph  from  memoir  of  H.  B.  Lemon.) 

PLATE  IV 


X-RAYS  AND  ATOMIC  NUMBERS          133 


periodic  table  there  will  be  absorption  by  all  elements 
of  atomic  numbers  lower  than  that  from  which  the 
radiation  arises. 

The  phenomenon  is  further  illustrated  in  Fig.  27. 
A  series  of  elements  were  exposed  to  the  K  radiation 
of  nickel  (atomic  number  28).  For  each  element 
the  height  of  the  curve  represents  the  absorption. 


A 


H 


/ 


K  Radiation 


r\ 


L  Racffah'on 


0  40  80  120  160  200  240 

Atomic  Weight  of  Absorbing  Element 

FIG.  27 

Relation  between  absorption  of  X-rays  and  atomic  weight  of 
absorbing  element.  4  The  K  type  radiation  from  Ni  (atomic 
weight  58.7)  was  successively  impressed  upon  various  elements. 
For  elements  below  Ni  it  excited  K,  L  and  M  radiations.  For 
elements  of  extremely  high  atomic  numbers  it  excited  only  M 
radiations;  for  the  intervening  elements  L  and  M  radiations. 

In  each  of  the  elements  below  nickel  there  is  an 
absorption  of  the  K  radiation  from  nickel,  for  in 
each  element  the  X-ray  energy  is  absorbed  by  the 
electronic  systems  which  then  vibrate  naturally  to 
give  off  their  own  radiation,  not  only  K  type  but  also 
L  and  M  types.  The  higher  the  atomic  number 
the  greater  the  amount  of  energy  required  to  emit 
the  characteristic  radiation  and  hence  the  greater 
the  absorption. 


134  WITHIN  THE  ATOM 

When  nickel  is  reached,  absorption  abruptly  ceases 
so  far  as  it  is  due  to  energy  which  is  converted  into 
characteristic  K  radiation.  There  remains,  how- 
ever, a  cause  of  absorption  in  the  L  and  M  types  of 
radiation.  These  vibrations  are  of  lower  frequency 
and  require  less  energy.  As  elements  of  still  higher 
numbers  are  examined  the  absorption  increases.  The 
"rare  earth'7  elements  have  not  been  examined,  so 
that  for  this  region  the  probable  form  of  the  curve  is 
indicated  by  dots.  For  some  element  in  this  range 
the  nickel  radiation  is  unable  to  excite  the  L  series 
but  may  excite  a  series  of  still  lower  frequencies 
known  as  M.  Again  the  absorption  increases  as  in- 
dicated in  the  figure. 

Studies  of  absorption  phenomena  by  DeBroglie 
and  others  are  largely  responsible  for  our  knowledge 
of  the  atomic  numbers  of  the  elements  of  higher 
atomic  weight.  A  great  deal  of  evidence,  however, 
besides  that  which  has  been  presented  in  this  chapter, 
confirms  the  modern  physicist  in  his  concept  of 
atomic  numbers. 


BETWEEN  CHAPTERS 

A  DIALOGUE 

IN  one  of  Stevenson's  fables  the  characters  of 
"Treasure  Island"  come  forth  between  chapters  to 
discuss  the  author's  plans  for  them.  For  writers  of 
less  ability  the  characters  adopt  tactics  of  heckling 
between  chapters.  In  the  present  book  there  are 
only  two  characters  if  one  does  not  include  the  form- 
less and  intangible  spirit  of  energy.  The  burden  of 
their  complaint  is  the  author's  selection  of  their 
characteristics.  For  some  time  Proton  and  Electron 
have  been  objecting  that  they  were  incompletely 
described. 

Proton  and  Electron:  Why  haven't  you  told  how 
large  we  are? 

Author:  I  have  by  implication.  You  are  too 
small  to  see  anyway. 

Electron:  We  don't  believe  you  know. 

Author:  What  if  I  don't  know  exactly?  You  can't 
be  greater  in  diameter  than  0.000,000,0 — 

Voice  of  Energy:  Stop!  You  are  not  paid  by 
space  rates.  If  you  will  degrade  me  and  decrease 
my  availability,  wasting  wood  pulp  by  the  page,  re- 
fusing even  to  make  the  small  conservation  of  my 
potentialities  which  simplified  spelling  offers,  you 
might  at  least  stop  writing  noughts.  Can't  you  use 
powers  of  ten?  Write  it  as  2X10'13  or  as  2/1013. 

Author:  Yes,  I  know;  but  it  will  make  my  pages 

135 


136  WITHIN  THE  ATOM 

look  mathematical  and  inhibit  the  General  Reader. 

General  Reader  (by  ether  waves):  Don't  mind 
me;  I  am  about  through  with  you  anyway. 

Scientific  Reader  (through  the  same  hypothetical 
medium):  I  am  through  with  you,  too.  You  have 
approached  the  subject  in  an  order  which  is  imprac- 
ticable for  pedagogical  purposes,  starting  with  un- 
known electrons  and  then  describing  how  they  were 
discovered.  Just  take  your  last  chapter.  You  beat 
all  around  the  subject  and  didn't  say  that  what 
Moseley  found  was  a  proportionality  between  the 
square  root  of  the  frequency  and  the  atomic  number. 

Voice  oj  Energy:  Don't  mind  that  fellow.  I  am 
the  only  important  entity  in  the  entire  physical  uni- 
verse. He  doesn't  really  know  me.  He  speaks  of 
me  glibly  at  times  but  when  he  gets  into  a  pinch  he 
says  its  due  to  some  kind  of  a  force — that's  his  way 
of  referring  to  me  when  I  am  getting  a  bit  run  down. 
Now,  as  to  you.  You  tell  me  when  you  are  going  to 
give  me  a  whole  chapter  to  myself.  You  are  ready 
to  do  it  now.  In  fact,  you  got  yourself  in  for  it  by 
flirting  with  my  Quanta  in  the  last  chapter. 

Electron:  Oh!  please,  Father  Energy,  you  know 
how  my  every  motion  conforms  to  your  first  and 
second  laws.  Don't  insist.  I  feel  sure  he  was  going 
to  discus§  emission  spectra  of  lower  frequencies  and 
then  he  would  be  discussing  oscillations  within  the 
visible  spectrum.  And  you  know  I  just  love  to  be 
seen  of  men.  Or,  perhaps  he  was  intending  to  de- 
scribe how  swiftly  I  can  fly  when  I  receive  from 
X-rays  or  ultra-violet  light  just  one  tiny  quantum. 
And  you  know,  Father  Energy,  he  couldn't  write 


BETWEEN  CHAPTERS  137 

half  a  chapter  on  the  photo-electric  effect  without 
saying  something  about  these  quanta  in  which  you 
are  so  much  interested. 

Proton:  That  argument  cuts  both  ways.  Why 
shouldn't  he  treat  us  both  alike?  You  know  its  our 
joint  motion  as  atoms  to  which  he  referred  once  as 
thermal  agitation.  If  he  will  write  now  about  that 
subject  he  can't  get  far  without  introducing  quanta. 
Father  Energy  himself  knows  that  Planck's  theory 
of  quanta  might  never  have  received  the  attention 
it  has  if  Einstein  hadn't  applied  it  to  the  problem 
of  specific  heats.  If  he  starts  with  the  motion  and 
energy  of  molecules  and  atoms  he  is  bound  to  give 
more  ideas  of  their  sizes  and  to  explain  how  scientists 
know  how  many  molecules  there  are  in  any  volume 
of  gas,  and  what  Avogadro's  constant  is,  anyway. 
And  then  he  can't  help  emphasizing  my  point  that 
even  if  you  are  larger  than  I  am,  still  I  am  much 
more  massive. 

Electron:  Yes,  you  are  more  massive,  but  what 
he  said  about  you  was  that  you  had  1845  times  as 
much  inertia  as  I  had.  I  don't  believe  he  appreciates 
personalities  like  yours  with  too  much  inertia. 
Didn't  he  give  you  a  new  name?  That  shows  he's 
radical  and  insulted  you,  too,  hanging  on  you  one 
of  those  newfangled  names  which  some  English 
scientists  have  only  just  suggested.  If  he  thought 
so  much  of  you  why  wasn't  he  respectful  enough  to 
call  you  a  "positive  electron"  as  all  good  scientists 
do? 

Voice  of  Energy:  Stop  quarrelling.  You  are  dis- 
sipating energy.  All  that  you  have  said  merely 


138  WITHIN  THE  ATOM 

shows  the  close  interrelation  .of  any  one  phenomenon 
of  physical  science  to  a  large  number  of  others.  What 
does  it  matter  to  which  portion  of  the  subject  he 
jumps  next?  Don't  you  realize  that  radioactive 
phenomena  and  now  my  quanta  have  shown  that 
nature  proceeds  per  saltumf  Really,  it  isn't  nearly 
as  important  where  he  jumps  as  how  he  lands. 

Proton:  Do  you  mean  that  I  must  go  back  and 
live  with  this  electron  in  some  dark  atomic  struc- 
ture? 

Electron:  If  it  isn't  dark  my  activities  will  pro- 
vide the  light. 

(Exeunt  Proton  and  Electron.) 

Author:  Well,  they're  gone.  But  what  was  that 
last  remark  of  Energy  as  to  how  I  am  going  to  land? 


CHAPTER  XI 

/ 

PHOTO-ELECTRIC  EFFECTS  AND  THE  QUANTUM  OF 
ENERGY 

Two  phenomena  are  observable  when  X-rays  im- 
pinge upon  a  substance.  X-rays  are  re-radiated  and 
electrons  are  ejected.  The  first  phenomenon,  which 
was  discussed  in  the  last  chapter,  has  served  to  estab- 
lish the  quantitative  relations  between  the  nuclei 
of  different  types  of  atomic  systems.  It  is  charac- 
teristic of  radiant  energy  of  all  frequencies.  Ac- 
cording to  the  frequency  of  the  original  vibration 
and  according  to  the  oscillating  systems  of  the  sub- 
stance upon  which  it  falls,  radiant  energy,  whether 
light  or  heat,  is  absorbed  and  re-radiated  with  or 
without  change  of  frequency.  Of  re-radiation  with 
change  of  frequency  an  illustration  in  the  visible 
range  of  frequencies  is  furnished  by  so-called  fluores- 
cent substances. 

Just  as  substances  exposed  to  X-rays  give  off  their 
own  characteristic  vibrations  when  these  are  of  lower 
frequency,  so  fluorescent  substances  when  exposed  to 
the  invisible  ultra-violet  radiations  will  give  off 
visible  radiations.  Electric  arc-lights  are  quite  rich 
in  ultra-violet  radiations,  so  that  fluorescent  sub- 
stances exposed  to  such  light  will  glow  with  their 
characteristic  radiations.  The  effect  is  easily  ob- 

139 


140  WITHIN  THE  ATOM 

served  also  with  sunlight,  if  a  beam  is  allowed  to  fall 
on  a  glass  vessel  of  kerosene.  If  the  vessel  is  viewed 
at  right  angles  to  the  beam  the  characteristic  blue 
fluorescence  of  the  kerosene  may  be  observed. 

The  second  phenomenon,  that  of  the  ejection  of 
electrons,  is  also  characteristic  of  all  radiations  within 
certain  limits  of  frequency.  Gamma  rays,  X-rays  and 
ultra-violet  light  will  all  eject  electrons  from  the 
substances  upon  which  they  fall.  The  limiting  fre- 
quencies below  which  such  ejection  cannot  occur  lie 
in  the  range  of  ultra-violet  and  even  visible  light  and 
depend,  as  we  shall  see,  upon  the  atomic  systems  of 
the  substance. 

A  picture  of  the  phenomenon  as  it  occurs  in  the 
case  of  X-rays  may  be  quoted  from  a  popular  lec- 
ture *  by  Sir  William  Bragg.  "Suppose  that  the 
target  (anti-cathode)  of  an  X-ray  bulb  were  magni- 
fied in  size  until  it  was  about  as  great  as  the  moon's 
disk,  that  is,  magnified  a  hundred  million  times.  The 
atoms  in  it  would  be  spheres  a  centimeter  or  so  in 
diameter,  but  the  electrons  (and  the  nuclei,  as  well) 
would  still  be  invisible  to  the  naked  eye.  The  actual 
distance  from  earth  to  moon  would  now  correspond 
roughly  to  the  corresponding  magnification  of  the 
distance  that  ordinarily  separates  the  bulb  from  the 
observer's  apparatus  (the  substance  under  examina- 
tion). We  now  shoot  electrons  (a  cathode  stream) 
at  the  moon  with  a  certain  velocity.  Let  us  say  that 
every  second,  each  square  foot  or  square  inch,  it 
doesn't  matter  which,  receives  an  electron.  A  radia- 

lrThe  Twelfth  Kelvin  Lecture  before  the  Institution  of  Elec- 
trical Engineers,  1921  (not  literally  quoted). 


THE  QUANTUM  OF  ENERGY      141 

tion  starts  away  from  the  moon,  which  immediately 
manifests  itself  by  causing  electrons  to  spring  out 
of  bodies  upon  which  it  falls.  They  leap  out  of 
the  earth,  here  one  and  there  one;  from  each  square 
mile  of  sea  or  land,  one  a  second  or  thereabouts. 
They  may  have  various  speeds  but  none  exceed, 
although  some  will  just  reach,  the  velocity  of  the 
original  electrons  that  were  fired  at  the  moon.  That 
reduced  again  to  normal  size  is  the  process  that  goes 
on  in  and  about  an  X-ray  bulb.  It  is  part  of  a 
universal  process  going  on  wherever  electron  or  wave 
falls  on  matter  and  is  one  of  the  most  important  and 
fundamental  operations  in  the  material  world." 

The  electrons  which  are  ejected  when  an  X-ray 
passes  through  a  substance  start  off  with  speeds  and 
energies  like  those  of  the  cathode  rays  which  origi- 
nated the  radiation.  As  they  pass  through  the  sub- 
stance they  disturb  other  electrons  and  hence  ionize 
large  numbers  of  the  atoms.  Except  for  such  dodging 
as  may  be  required  to  avoid  adjacent  systems  the 
ejected  electrons  move  at  right  angles  to  the  direc- 
tion of  the  beam.  Their  paths  have  been  photo- 
graphed by  C.  T.  R.  Wilson,  using  his  discovery  of 
cloud  formation  in  humid  atmosphere.  In  Fig.  28 
is  shown  the  path  of  an  X-ray  through  a  gas.  It  is 
marked  by  the  activities  of  the  electrons  which  it 
ejects.  Their  trails  of  ionized  atoms,  as  shown  by 
the  drops,  start  at  right  angles  to  the  path  of  the 
ray,  which  is  lengthwise  through  the  center  of  the 
picture. 

The  phenomenon  of  the  ejection  of  electrons,  when 
the  exciting  radiation  is  ultra-violet  or  lies  within  the 


142  WITHIN  THE  ATOM 

visible  range,  is  known  as  the  photo-electric  effect. 
It  promises  to  be  of  wide  scientific  interest,  for  it  is 
apparently  the  cause  of  photo-chemical  effects  like 
those  utilized  in  photography,  of  photo-synthesis  in 
the  formation  of  carbohydrates  hi  plant  life,  and 
even  of  the  effect  of  light  on  the  retina  of  the  eye. 

When  light  of  a  certain  minimum  frequency  is 
incident  upon  a  substance  electrons  may  be  ejected. 
The  phenomenon  was  first  noticed  by  Hallwachs  in 
1888,  who  found  that  a  metal  plate  became  posi- 
tively charged,  or  lost  its  negative  charge,  if  it  were 
originally  negative.  This  is  what  should  happen  if 
electrons  are  emitted  by  the  plate. 

Present-day  theories  as  to  this  effect  are  the  re- 
sult of  observations  by  a  large  number  of  experi- 
menters, to  which  a  valuable  addition  was  made  by 
Einstein  in  terms  of  the  quantum  theory.  This 
theory,  which  received  some  mention  on  page  119, 
was  propounded  by  Planck  about  1901  to  explain 
certain  phenomena  of  radiation  with  which  we  shall 
deal  later.  In  1905  Einstein  applied  it  to  photo- 
electric effects  and  predicted  that  the  emission  of 
electrons  would  conform  to  a  simple  relation. 

He  assumed  that  the  electron,  which  is  emitted, 
leaves  the  metal  as  the  result  of  its  absorption  from 
the  incident  radiation  of  one  quantum  of  energy.  A 
quantum,  as  has  been  said,  is  a  small  amount  of 
energy,  numerically  equal  to  the  product  of  Planck's 
constant,  h,  and  the  frequency,  n,  of  the  radiation, 
and  hence  symbolized  as  hn.  The  energy  with  which 
the  electron  leaves  the  surface  is  less  than  the  ab- 
sorbed energy,  hn,  by  the  amount  expended  in  get- 


THE  QUANTUM  OF  ENERGY      143 

ting  free  from  the  atom,  much  as  the  energy  of  a 
bullet  at  the  muzzle  of  a  gun  is  less  than  that  con- 
tributed to  it  by  the  explosion  because  of  the 
frictional  losses  in  the  barrel.  For  any  substance 
there  will  be,  then,  a  frequency  of  radiation,  n0)  such 
that  the  quantum  contributed  to  the  electron  just 
represents  the  energy  required  to  set  it  free  of  its 
former  associates.  For  a  quantum  at  this  frequency 
it  becomes  free  but  is  too  exhausted  to  move  beyond 
the  threshold.  For  any  exciting  frequency,  as  n, 
which  is  higher  than  this  threshold  frequency,  n0,  the 
electron  will  have  a  net  balance  of  kinetic  energy 
which  it  may  expend  beyond  the  confines  of  its 
atomic  home.  This  balance  is  always  equal  to  the 
difference  of  two  quanta,  one  of  value  hn  and  the 
other  hn0. 

This  is  Einstein's  relation.  At  the  tune  he  made 
his  prediction  there  was  no  experimental  evidence 
that  the  kinetic  energy  with  which  electrons  are 
emitted  should  increase  proportionately  with  the 
frequency,  n,  of  the  light.  The  relation  has  been 
verified  since  and  this  successful  application  of  the 
quantum  theory  is  strong  evidence  for  the  correct- 
ness of  the  hypothesis  of  quanta. 

One  of  the  most  exhaustive  investigations  of  Ein- 
stein's expression  was  carried  out  by  Millikan.  Not 
only  did  he  verify  the  relationship  but  he  obtained 
from  his  experimental  data  a  very  exact  value  for 
Planck's  constant,  h.  He  measured  frequencies  and 
energies  and  hence  h,  the  other  magnitude  involved 
in  the  relationship,  was  determined.  The  fact  that 
it  was  constant,  independent  of  the  frequency  of 


144  WITHIN  THE  ATOM 

the  exciting  light,  was  the  proof  of  the  correctness 
of  the  relation  under  examination.  The  method  fol- 
lowed was  essentially  that  of  previous  investigators 
of  the  photo-electric  effect.  The  accuracy  of  Milli- 
kan's  determination  of  h  lies  partly  in  the  precision 
of  his  observations  and  partly  in  his  use,  for  the 
calculation  of  h,  of  the  modern  value  for  the  charge 
represented  by  an  electron,  which  he  had  determined 
by  the  oil-drop  method. 

The  quantity  of  electricity  represented  by  an  elec- 
tron enters  into  the  relationship  because  of  the  ex- 
perimental method  which  was  followed  in  determin- 
ing the  energy  of  the  emitted  electron.  Suppose  the 
plate  or  electrode  which  is  to  be  exposed  to  the  radia- 
tion is  made  positive  with  respect  to  its  surroundings 
by  connecting  between  them  a  battery.  The  plate 
then  starts  with  a  deficiency  of  electrons  and  its  sur- 
roundings have  an  excess.  If  an  electron  is  moved 
from  the  positive  plate  to  a  nearby  object  it  will 
acquire  a  certain  amount  of  potential  energy.  In 
order  that  it  shall  of  itself  perform  such  a  motion 
it  must  leave  the  plate  with  a  kinetic  energy  at  least 
equal  to  this  potential  energy  which  it  will  have  at 
the  completion  of  its  journey.  By  adjusting  the 
potential  applied  by  the  battery  to  a  value  just  be- 
yond the  possibilities  of  the  emitted  electron  the 
latter  may  be  just  prevented  from  reaching  any 
of  its  negative  surroundings.  The  value  of  the  po- 
tential energy  of  an  electron  on  the  negative  body 
then  measures  the  kinetic  energy  of  the  emitted 
electron. 

Into  the  evaluation  of  this  potential  energy  there 


THE  QUANTUM  OF  ENERGY      145 

enters  the  charge  on  an  electron.  You  will  remem- 
ber that  for  simplicity  we  took  the  electron  as  the 
unit  of  electricity  and  the  potential  energy  of  an 
electron  as  the  unit  of  electrical  potential.  The  pres- 
ent accepted  units  of  charge  and  potential  were 
adopted,  however,  before  the  electron  was  discovered. 
The  unit  of  electrical  potential  is  the  potential 
energy  of  unit  charge,  but  unit  charge  is  not  the 
electron.  Hence,  to  express  the  potential  energy  of 
an  electron  in  the  accepted  units  one  must  know  the 
relation  between  unit  charge  and  the  electronic 
charge.  This  relationship  Millikan  had  determined 
very  accurately  by  the  method  described  on  page  94. 

The  photo-electric  experiment  was  performed  in 
a  highly  evacuated  vessel  for  collisions  with  gas 
molecules  would  mask  the  effect.  The  substances 
used  were  the  alkali  metals,  lithium,  sodium,  and 
potassium,  which  are  very  markedly  electropositive. 
Their  atoms  each  have  one  more  electron  than  is 
desirable  for  a  stable  configuration  and  probably 
for  this  reason  they  are  most  sensitive.  They  will 
respond  to  the  frequencies  of  the  visible  spectrum 
as  well  as  to  the  ultra-violet  frequencies. 

Cylindrical  plates  of  these  materials  were  mounted 
as  shown  in  Fig.  29,  so  that  one  at  a  time  could  be 
studied.  By  magnetic  control  from  outside  the  ves- 
sel a  plate  could  be  turned  to  the  knife  S,  which  re- 
moved a  thin  paring  and  left  a  fresh  surface.  The 
plate  with  its  clean  surface  was  then  turned  into  con- 
tact with  electrode  C,  so  as  to  determine  what  por- 
tion of  its  potential  was  due  to  the  so-called  "con- 
tact electromotive  force,"  that  is  to  differences  in 


146 


WITHIN  THE  ATOM 


potential  which  are  always  present  between  dissimi- 
lar substances.  It  was  then  turned  to  face  the  wire 
gauze  cylinder  G,  which  effectively  constituted  its 
surroundings.  Whether  or  not  any  electrons  reached 
this  cylinder  was  determined  by  observing  an  elec- 
trometer connected  to  it  at  B. 


FIG.  29 

Cross-section  of  Millikan's  apparatus  for  measuring  photo- 
electric emission.  Light  entering  at  0  ejects  electrons  from  the 
disc  Na.  If  these  reach  the  wire  gauze  cylinder,  G,  a  deflection 
is  produced  in  an  electroscope  connected  to  the  terminal  B. 

The  value  of  h  which  was  obtained  will  be  given 
in  the  Appendix  with  other  important  physical 
magnitudes,  since  statements  of  magnitude  involve 
choices  of  units  and  in  the  case  of  scientific  units  con- 
siderable explanation  is  usually  required. 


THE  QUANTUM  OF  ENERGY     147 

Millikan  also  verified  a  phenomenon,  first  ob- 
served by  Lenard  in  1902,  which  was  implicitly 
covered  by  our  earlier  discussion  of  Einstein's  appli- 
cation of  the  quantum  theory  to  photo-electric  emis- 
sion. The  energy  with  which  the  electron  is  ejected 
depends  only  upon  the  substance  and  the  frequency. 
It  is  independent  of  the  intensity  of  the  light  which 
causes  the  ejection.  If  the  light  is  intense  more 
electrons  are  emitted  but  none  leaves  with  greater 
energy.  This  same  phenomenon  also  occurs  in  the 
case  of  X-rays  and  of  gamma  rays.  The  amount  of 
light  determines  the  number  of  electrons  which  are 
ejected  but  does  not  affect  their  individual  energies. 

For  X-rays  the  converse  phenomenon  has  been  in- 
vestigated. Duane  and  Hunt  and  also  Hull  have 
studied  X-ray  radiation  and  found  that  the  highest 
frequency  in  the  general  or  "white"  radiation  corre- 
sponds to  that  which  should  arise  according  to  the 
quantum  theory.  The  product  of  this  highest  fre- 
quency by  Planck's  constant  is  always  equal  to  the 
energy  of  the  individual  electrons  in  the  cathode 
stream  which  causes  the  radiation. 

From  all  these  experiments  it  seems  certain  that 
whenever  electronic  impacts  give  rise  to  radiation 
the  energy  associated  therewith  is  always  propor- 
tional to  the  frequency  and  the  factor  of  propor- 
tionality is  Planck's  constant,  h.  Similarly,  it  appears 
from  all  measurements  where  electrons  are  emitted 
by  radiant  energy  that  the  energy  associated  with 
the  individual  electrons  is  always  related  to  the  fre- 
quency of  the  radiation  by  this  same  constant.  The 
result  is  that  the  scientific  world  has  quite  unani- 


148  WITHIN  THE  ATOM 

mously  accepted  it  to  be  a  fact  that  energy  is  emitted 
in  quanta. 

When  an  electronic  system  expends  energy  it  does 
so  in  definite  amounts.  Is  energy  granular  or  atomic 
in  character?  Must  we  think  of  it  as  transmitted 
through  space  like  a  corpuscle?  And  then,  is  each 
corpuscle  of  energy  received  in  to  to  by  a  single  elec- 
tron? Since  an  electron  can  emit  only  definite 
quanta  of  energy,  can  it  receive  energy  in  amounts 
less  than  a  quantum?  If  it  receives  and  emits  only 
by  quanta,  presumably  its  own  total  energy  at  any 
time  is  some  integral  number  of  quanta.  What  in 
any  case  is  the  mechanism  which  is  involved? 

Such  are  the  questions  which  confront  the  scien- 
tist of  today.  Evidence  as  to  the  correct  answers  is 
lacking  but  it  may  well  be  forthcoming  in  the  near 
future.  Such  evidence  as  now  exists  only  makes  the 
problem  more  complicated.  Consider,  for  example, 
the  question  as  to  the  absorption  of  energy. 

The  moment  a  substance  is  exposed  to  light  of  the 
proper  frequency  the  photo-electric  emission  begins. 
This  would  appear  to  indicate  that  there  was  a  hop- 
perful  of  energy  in  some  electronic  system  which 
was  tripped  off,  as  by  a  trigger,  and  allowed  to  dis- 
charge. The  energy  which  is  released  was  either  ob- 
tained from  the  beam  of  light,  despite  the  short  time 
of  exposure,  or  was  already  stored  in  the  atomic  sys- 
tem. The  further  fact  that  the  energy  of  the  emitted 
electron  is  the  same  whether  the  intensity  of  the 
light  is  large  or  small  would  seem  to  indicate  such  a 
storage.  Photo-electric  phenomena  occur  in  such 
feeble  light  as  would  correspond  to  an  ordinary 


THE  QUANTUM  OF  ENERGY      149 

candle  at  a  distance  of  three  miles.  (The  number 
of  electrons  which  are  emitted  each  second  is  greater 
for  greater  light  intensity  even  though  the  energy  of 
each  is  a  function  only  of  the  frequency.)  Through- 
out the  entire  range  of  intensities,  which  would  corre- 
spond to  bringing  the  candle  from  miles  away  to 
within  an  inch  of  the  plate,  the  energy  of  an  emitted 
electron  is  always  one  quantum. 

For  the  moment,  then,  the  evidence  adduced  seems 
to  favor  a  theory  of  continuous  absorption  of  energy, 
its  storage,  and  release  in  quanta  when  the  electronic 
oscillator  is  disturbed.  But  if  there  is  such  a  trigger 
action  why  should  the  action,  and  the  amount  of 
energy  which  is  released,  depend  upon  the  exciting 
frequency?  One  might  think  of  a  tuned  system 
which  responded  only  to  a  single  note,  but  why 
should  the  amount  of  the  response  depend  upon  the 
note?  It  should  make  no  difference  what  frequency 
of  radiation  disturbs  the  hopper  and  allows  it  to 
dump  its  load  of  energy.  Why,  also,  should  the  out- 
put depend  solely  upon  the  frequency  and  not  upon 
the  type  of  hopper,  that  is  upon  the  type  of  atom? 
It  does,  although  the  amount  of  energy  which  is  ex- 
pended by  the  emitted  electron  in  passing  through 
surrounding  systems  does  depend  upon  the  atomic 
nature  of  the  substances.  The  analogy  of  the  hopper 
which  is  released  by  a  trigger  action  seems  to  be 
contrary  to  the  observed  facts.  We  are  forced,  there- 
fore, to  the  conclusion  that  the  energy  of  the  escap- 
ing electrons  is  derived  from  the  incident  light. 

But  this  conclusion  brings  us  back  to  the  difficulty 
as  to  the  intensity  of  the  light  which  excites  the 


150  WITHIN  THE  ATOM 

effect.  According  to  the  theory  of  radiation  which 
is  commonly  accepted,  the  energy  leaving  a  source  is 
uniformly. distributed  over  a  spherical  surface  which 
increases  constantly  in  size  as  the  radiation  proceeds 
outward.  The  effect  may  be  seen  in  the  widening 
circle  of  a  wave  caused  by  dropping  a  stone  into 
water.  An  object  upon  which  such  a  wave  front 
impinges  subtracts  from  it  only  the  energy  corre- 
sponding to  the  proportion  of  the  total  wave  front 
which  strikes  the  object.  The  effect  is  well  known 
to  sailors  of  small  boats  who  have  received  the  wash 
of  a  steamer  before  its  wave  front  was  much  en- 
larged. If  we  calculate  on  this  basis  the  amount  of 
radiant  energy  which  in  one  second  should  reach  a 
tiny  atom  we  find  cases  where  the  amount  is  so 
small  that  billions  of  seconds  would  be  required  be- 
fore the  atom  could  acquire  the  quantum  of  energy 
which  it  radiates  so  promptly. 

This  difficulty  would  be  solved  if  energy  were  not 
resident  in  the  medium,  as  it  is  in  the  obvious  me- 
chanical case  of  the  water  wave,  but  had  a  corpuscu- 
lar structure.  On  this  basis,  when  a  body  radiated 
energy  it  would  really  be  shooting  out  in  all  direc- 
tions a  shower  of  invisible  particles,  small  bundles 
of  energy.  The  electron  must  then  receive  or  reject 
a  whole  bundle.  The  picture  of  the  ejection  of  elec- 
trons by  X-rays  which  was  quoted  on  page  140  would 
be  explained  if  the  X-rays  were  really  small  bullets 
of  energy  which  followed  radial  paths  outward  from 
the  anti-cathode.  What  appears  to  us  as  a  continu- 
ous distribution  of  energy  in  a  wave  is  probably  not 
really  continuous  but  conforms  in  analogy  to  a  fine 


THE  QUANTUM  OF  ENERGY  /    151 

shower  of  rain  such  as  one  experiences  when  a  fog 
blows  in. 

Matter  which  originally  appeared  to  mankind  as 
continuous  and  infinitely  divisible  has  been  shown  to 
be  atomic.  Electricity,  whose  phenomena  appeared 
those  of  an  invisible  fluid,  has  proved  to  be  granular 
in  structure.  Why  should  we  not  expect  that  energy 
also  should  prove  to  be  not  infinitely  divisible  but 
transmissible  only  in  finite  amounts?  There  are 
three  objections:  First  is  the  incompleteness  of  the 
evidence,  second  the  subconscious  effects  of  our  sci- 
entific traditions  and  training,  and  third,  a  definite 
piece  of  evidence  against  the  hypothesis  which  as 
yet  has  not  been  explained  away. 

A  corpuscular  theory  for  light  was  commonly  ac- 
cepted in  Newton's  time,  despite  a  growing  mass  of 
evidence  and  theory  in  favor  of  a  wave  motion 
through  an  ethereal  medium.  Reflection  was  then 
explained  as  due  to  an  attraction  of  the  reflecting 
surface  which  bent  toward  itself  the  swiftly  moving 
corpuscle,  which  the  human  eye  later  apperceived  as 
light.  As  it  happens,  our  present  concept  of  reflec- 
tion as  re-radiation  would  also  accord  with  a  corpus- 
cular theory  for  the  transmission  of  energy  through 
space. 

The  evidence  which  finally  dispossessed  the 
corpuscular  theory  arose  in  connection  with  the  phe- 
nomenon of  interference.1  In  its  simplest  form  in- 
terference phenomena  take  place  as  illustrated  in 

JWe  have  already  implicitly  applied  the  theory  of  this  phe- 
nomenon to  the  case  of  the  crystal  grating  for  the  spectral 
analysis  of  X-rays. 


152 


WITHIN  THE  ATOM 


Fig.  30.  Imagine  a  source  of  radiant  energy  to  trans- 
mit to  two  slits,  shown  in  cross  section  at  a  and  b. 
From  these  two  slits  the  energy  spreads  through  the 
ether  just  as  if  the  slits  were  separate  homogeneous 
sources.  For  simplicity  we  imagine  the  light  to  be  a 
single  frequency.  From  these  slits  there  then  spread 
out  a  succession  of  wave  surfaces.  In  cross  section 
these  have  much  the  appearance  of  surface  waves 


FIG.  30 
Diagram  illustrating  interference  of  wave  trains. 

which  are  produced  in  liquids  by  regularly  recurring 
disturbances.  Where  the  trough  of  one  meets  the 
crest  of  another,  interference  occurs.  Where  trough 
coincides  with  trough,  or  crest  with  crest,  there  is  re- 
enforcement  and  a  greater  displacement.  The  figure 
represents  an  instantaneous  view  of  the  transmission 
and  shows  crests  as  full  lines  and  troughs  as  dotted 
lines. 

It  is  easy  to  pick  out  a  succession  of  points  where 


THE  QUANTUM  OF  ENERGY      153 

either  type  of  interference  phenomenon  is  occurring. 
At  some  point  like  Y,  for  example,  the  disturbance 
from  a  is  three  whole  wave  lengths  ahead  of  that 
from  b,  and  reenforcement  occurs. 

In  the  present  case  there  is  a  definite  limit  to  the 
number  of  wave  lengths  by  which  the  two  disturb- 
ances can  differ.  With  the  interferometer,  however, 
which  was  devised  by  Michelson,  large  differences  in 
path  may  be  obtained.  Differences  of  as  much  as 
several  thousand  wave  lengths  have  been  instituted 
between  the  paths  of  the  beams  from  two  homo- 
geneous sources  and  still  the  phenomenon  of  inter- 
ference has  been  observable. 

The  objection  of  the  necessity  of  conforming  to 
the  known  facts  of  interference  is  not,  however,  un- 
surmountable.1  It  would  seem  to  demand  that  the 
bundle  of  energy  should  have  a  length  which  might 
be  large  in  terms  of  wave  length  but  would  be  small 
as  compared  to  the  distance  the  energy  travels  in 
each  second.  In  some  way  this  bundle  might  also 
contain  within  itself  something  of  the  structure  of  a 

1  It  may  well  be  that  the  two  aspects  of  radiant  energy  which 
we  recognize  as  "quantum"  and  as  "wave  motion"  are  not 
mutually  incompatible.  Such  a  possibility  is  noted  by  way  of 
illustration  in  that  most  interesting  book  on  relativity,  Professor 
Eddington's  "Space,  Time  and  Gravitation."  He  says,  "Physical 
reality  is  the  synthesis  of  all  possible  physical  aspects  of  nature. 
An  illustration  can  be  taken  from  the  phenomena  of  radiant 
energy  or  light.  In  a  very  large  number  of  phenomena,  the  light 
coming  from  an  atom  appears  to  be  a  series  of  spreading  waves. 
In  many  other  phenomena  the  light  appears  to  remain  a  minute 
bundle  of  energy,  all  of  which  can  enter  and  explode  a  single  atom. 
There  may  be  some  illusion  in  these  experimental  deductions; 
but  if  not,  it  must  be  admitted  that  the  physical  reality  cor- 
responding to  light  must  be  some  synthesis  comprehending  both 
these  appearances.  How  to  make  this  synthesis  has  heretofore 
baffled  conception.  But  the  lesson  is  that,  .  .  .  reality  is  only  ob- 
tained when  all  conceivable  points  of  view  have  been  combined." 


154  WITHIN  THE  ATOM 

train  of  waves  which  would  produce  interference 
effects  with  bundles  which  had  been  dispatched  by 
other  routes. 

In  the  absence  of  direct  evidence  some  incline 
toward  one  side  and  some  toward  the  other  of  this 
question.  Perhaps  the  lay  reader  will  have  less  to  un- 
learn in  the  future  if  he  accustoms  himself  to  think 
of  there  being  shot  about  in  the  physical  universe 
bundles  of  energy,  the  arrival  and  departure  of  which 
are  manifested  by  changes  in  atomic  systems. 


CHAPTER  XII 

LIGHT  RADIATION  AND  ATOM-MODELS 

THE  concept  of  an  atom  with  a  nucleus  was  due 
to  Rutherford  whose  experiments  on  the  scattering 
of  alpha  rays  were  explainable,  as  we  have  seen  on 
page  102,  by  the  assumption  of  such  an  atomic  struc- 
ture. In  terms  of  this  structure  it  then  became 
necessary  to  explain  other  known  phenomena,  par- 
ticularly that  of  the  radiation  of  light  from  atoms. 
The  attempt  was  made  by  Bohr  in  the  years  immer 
diately  following  1913. 

He  started  by  pointing  out  that  the  planetary  eled- 
trons  of  the  Rutherford  atom-model  would  be  un- 
stable, according  to  the  recognized  laws  of  mechanics, 
if  their  rotation  was  assumed  to  be  the  cause  of  light 
radiation.  Rotating  electrons,  as  was  mentioned  on 
page  78,  influence  other  electrons.  In  so  doing  they 
impart  some  of  their  energy.  Consider  for  a  moment 
what  the  effect  would  be  if  the  rotation  of  the  planet- 
ary electrons  was  accompanied  by  a  radiation  of 
energy. 

Electron  and  nucleus  tractate,  but  the  kinetic 
energy  of  the  electron  prevents  its  falling  into  the 
nucleus,  just  as  planets  maintain  stable  paths  about 
the  sun  by  virtue  of  their  kinetic  energy.  If,  how- 
ever, this  energy  is  gradually  subtracted  by  radia- 

155 


156  WITHIN  THE  ATOM 

tion,  the  electron  will  fall  in  towards  the  nucleus. 
Due  to  its  changed  orbit  it  will  have  a  changed  fre- 
quency of  rotation.  A  continuous  change  in  fre- 
quency, therefore,  should  be  noted  in  the  light  from 
a  tube  of  gas  like  hydrogen  through  which  an  electric 
current  is  being  passed  by  the  motion  of  the  ionized 
gas  molecules.  No  such  change  is  noted,  for  the 
spectral  lines  of  the  chemical  elements  are  definite, 
unvarying,  and  characteristic. 

So-called  classical  electro-magnetic  theory  is  in- 
capable of  accounting  for  radiation  in  terms  of 
planetary  electrons  rotating  about  a  nucleus.  Bohr, 
therefore,  applied  to  the  phenomenon  the  quantum 
hypothesis  which  had  already  served  good  purposes 
in  other  fields  of  inquiry.  His  radical  assumption  is 
the  possibility  of  non-radiating  orbits.  In  the 
Rutherford-Bohr  atom-model  a  planetary  electron 
rotates  without  the  emission  or  absorption  of  energy. 
It  has  a  steady  orbital  motion  which  represents  a 
condition  of  equilibrium  so  far  as  concerns  changes 
in  energy. 

An  electron  may,  however,  be  caused  to  change 
its  orbit  and  the  emission  or  absorption  of  energy  is 
assumed  to  accompany  this  change  from  ,one 
equilibrium  state  to  another.  During  the  change  of 
an  electron  from  a  larger  to  a  smaller  orbit  radiation 
of  a  definite  frequency  is  emitted  and  the  amount 
of  energy  involved  is  always  one  quantum.  By  such 
a  theory  it  was  presumed  that  the  spectral  lines  of 
the  various  elements  could  be  accounted  for.  Char- 
acteristic spectra  are  emitted  by  the  various  ele- 
ments, as  we  have  seen  in  Chapter  XI,  when  the 


LIGHT  RADIATION  AND  ATOM-MODELSf    157 

electronic  structures  are  disturbed  by  the  impacts 
of  a  cathode  stream.  Vibration  frequencies  of 
smaller  values,  corresponding  to  the  ultra-violet  and 
visible  range,  arise  from  less  violent  disturbances, 
such  as  occur  for  example  in  the  ionized  gas  or  vapor 
of  a  highly  evacuated  tube  which  is  conducting  elec- 
tricity. 

When  an  electric  current  is  passed  through  a  gas 
light  is  emitted.1  By  using  a  spectrometer  or  a  grat- 
ing, involving  the  principles  of  interference  which 
have  been  mentioned  in  previous  chapters,  this  light 
may  be  analysed  into  a  series  of  spectral  lines,  simi- 
lar to  but  more  numerous  than  those  appearing  in 
an  X-ray  spectrum.  It  is  found  that  any  element 
produces  a  spectrum  in  which  lines  recur  at  intervals 
throughout  a  given  frequency  range.  These  lines 
form  a  series,  the  frequency  of  each  member  of  which 
may  be  calculated  from  that  of  the  highest  frequency 
by  very  simple  arithmetic.  In  the  case  of  incandes- 
cent hydrogen  three  such  series  are  known:  one  in 
the  visible  range  of  frequency  called  the  Balmer 
series;  one  in  the  region  of  lower  frequency,  the 
infra-red  region,  which  is  known  as  the  Paschen 
series;  and  the  third,  known  as  the  Lyman  series,  in 
the  ultra-violet. 

When  one  knows  the  highest  frequency  of  a  series 
of  spectral  lines  the  calculation  of  the  other  fre- 
quencies is  a  piece  of  arithmetic  which  impresses  one 
with  the  probability  that  the  order  of  nature  is  in- 

1  Energy  is  absorbed  from  the  source  of  electric  current  in  the 
act  of  ionization  and  radiated  when  recombination  occurs. 


158  WITHIN  THE  ATOM 

herent  in  the  granular  structure  of  electricity  and 
energy. 

Start  with  the  simple  series  of  numbers,  1,  2,  3,  4, 
5  and  so  on.  Write  the  reciprocals  of  these,  thus, 
1,  1/2,  1/3,  1/4.  Then  write  the  squares  of  these 
reciprocals,  thus,  1,  1/4,  1/9,  1/16.  Now  assume 
that  we  know  for  any  atomic  system  its  highest 
possible  frequency  of  radiation.  As  a  matter  of  fact, 
it  is  a  little  over  three  million,  million,  million,  and 
is  known  as  the  Rydberg  constant.  To  find  the 
lowest  frequency  we  take  the  difference  between  1 
and  1/4  and  multiply  it  into  this  constant  frequency. 
We  thus  obtain  the  line  of  longest  wave  length.  For 
the  next  line  of  this  same  series  we  multiply  the 
Rydberg  constant  by  the  difference  between  1  and 
1/9,  and  so  on  for  the  other  lines  of  the  Lyman 
series. 

The  Balmer  series,  which  has  its  head  (highest 
frequency)  in  the  visible  spectrum,  is  found  by  tak- 
ing the  second  number  of  the  series  of  squared 
reciprocals,  namely  1/4  and  subtracting  from  it  the 
next,  namely  1/9,  and  then  proceeding  as  before. 
For  the  third  series,  which  has  a  head  of  still  smaller 
frequency,  we  start  with  the  third  term,  and  subtract 
from  it  successively  the  fourth,  fifth,  and  succeeding 
terms. 

These  series  involve  a  relatively  large  number  of 
terms.  For  example,  in  the  spectra  of  certain  celestial 
bodies  thirty-three  hydrogen  lines  have  been  ob- 
served which  correspond  to  those  calculated  for  the 
Balmer  series.  Fig.  31  (Plate  IV,  opposite  p.  131) 
shows  a  photograph  of  a  hydrogen  spectrum.  In  the 


LIGHT  RADIATION  AND  ATOM-MODELS    159 

laboratory,  however,  only  twelve  lines  of  the  series 
are  reproducible  by  discharging  electricity  through 
a  tube  containing  a  little  hydrogen  gas. 

According  to  the  Bohr  theory  the  higher  the  num- 
ber in  the  series  the  greater  will  be  the  radius  of  the 
electronic  orbit.  The  greater  this  orbit  the  greater 
is  the  apparent  size  of  the  atom,  as  was  pointed  out 
on  page  13.  If,  therefore,  atoms  are  to  have  large 
electronic  orbits  their  centers  must  be  widely  sepa- 
rated, and  hence  the  gas  density  must  be  small. 

At  ordinary  atmospheric  pressure,  however,  the 
molecules  in  a  gas  are  relatively  close  together.  As 
the  number  in  any  enclosure  is  reduced  the  pressure 
which  they  exert,  or,  what  is  equivalent,  the  external 
pressure  necessary  to  constrain  them  to  this  volume, 
is  correspondingly  reduced  and  the  average  distance 
between  molecules  is  increased.  With  the  modern 
vacuum  pump  the  number  of  molecules  in  a  given 
vessel  may  be  so  reduced  that  on  the  average  indi- 
vidual molecules  will  travel  twenty  miles  between 
collisions  with  other  molecules  within  the  tube.  (Of 
course  we  are  not  considering  reflecting  collisions 
with  the  molecules  of  the  walls.)  Under  these  con- 
ditions, despite  the  fact  that  the  tube  will  still  con- 
tain about  a  thousand  million  molecules  in  each 
cubic  centimeter,  the  average  distance  between  mole- 
cules is  enormously  greater. 

Only  in  a  highly  evacuated  tube  would  there  be 
the  possibility  of  large  electronic  orbits.  The  cor- 
responding spectral  lines  are  not  visible,  however, 
because  the  whole  mass  of  the  gas  in  the  tube 
is  insufficient  to  give  sufficient  intensity  of  ra- 


160  WITHIN  THE  ATOM 

diation  to  permit  detection.  In  the  neighborhood 
of  stars,  on  the  other  hand,'  the  mass  of  the  gas  is 
sufficient  and  its  rarefied  condition  meets  the  re- 
quirement as  to  gas  density  so  that  lines  correspond- 
ing to  larger  orbits  may  be  observed.  On  the  basis 
of  the  Bohr  theory,  therefore,  the  failure  of  experi- 
menters in  the  laboratory  to  reproduce  or  to  observe 
the  higher  frequencies  of  the  Balmer  series  becomes 
explainable. 

Apparently,  also,  there  is  no  normal  size  for  any 
atom.  Its  effective  diameter  depends  upon  the  larg- 
est orbit  of  its  electrons.  Whether  or  not  an  electron 
moves  into  a  larger  orbit  depends  upon  the  restrain- 
ing effect  of  neighboring  systems  and  upon  the 
violence  of  the  disturbance  to  which  it  is  subjected. 

The  smaller  orbits  are  more  stable  because  of  the 
greater  tractation  between  nucleus  and  electron. 
Hence  an  electron  which  has  been  displaced  to  a 
larger  orbit  returns  to  one  of  smaller  size  and  greater 
stability.  In  so  doing  it  radiates  a  quantum  of 
energy  and  the  value  of  the  frequency  which  de- 
termines that  quantum  is  apparently  that  of  the  or- 
bit which  it  assumes.  For  large  displacements  the 
electron  may  assume  successively  smaller  and  smaller 
orbits  and  thus  give  rise  to  a  succession  of  lines  in  a 
spectral  series. 

When  a  large  number  of  atoms  are  involved,  as 
there  must  be  if  a  measurable  effect  is  to  be  observed, 
individual  atoms  may  be  emitting  different  charac- 
teristic frequencies.  To  the  observer,  however,  there 
appears  a  number  of  lines  of  the  series,  just  as  if  they 
were  simultaneously  produced  by  a  single  atom.  The 


LIGHT  RADIATION  AND  ATOM-MODELS    161 

fact  that  they  are  intermittent  and  originate  in 
separate  atoms  is  obscured,  since  he  deals  with  them 
statistically  in  terms  of  average  effects. 

Bohr's  method  and  its  successes  may  now  be 
briefly  summarized.  He  dealt  most  successfully 
with  the  hydrogen  atom  which  has  only  a  single 
electron  and,  therefore,  the  simplest  possible  struc- 
ture. Upon  the  assumption  of  non-radiating  or- 
bits he  was  able  to  apply  to  the  motions  of  electrons 
in  such  orbits  the  same  mechanical  principles  as  hold 
in  the  case  of  planetary  rotations  in  celestial  systems. 
By  the  adoption  of  the  quantum  hypothesis  he  was 
enabled  to  calculate  the  energy  changes  involved  in  a 
change  from  one  non-radiating  orbit  to  another.  In 
calculations  he  had  at  his  disposal  previously  ob- 
tained values  for  the  mass  of  an  electron,  for  its 
charge,  and  for  Planck's  constant.  In  terms  of  these 
he  calculated  the  diameter  of  a  hydrogen  atom  and 
the  corresponding  frequency  of  an  electron  revolving 
hi  this  orbit.  He  also  calculated  the  amount  of 
energy  required  to  displace  an  electron  completely 
from  the  hydrogen  atom  and  thus  found  the  poten- 
tial necessary  for  the  ionization  of  hydrogen.  His 
values  agreed  very  well  with  those  obtained  by  other 
means. 

He  further  calculated,  on  the  basis  of  his  theory, 
the  Rydberg  constant  for  hydrogen.  The  value  thus 
derived  differed  only  one  per  cent  from  that  obtained 
by  a  study  of  spectra.  At  that  time  the  head  of  the 
Lyman  series  had  not  been  discovered,  and  its  exist- 
ence was  in  effect  predicted  by  the  Bohr  analysis. 


162  WITHIN  THE  ATOM 

Similar  successes l  also  accompanied  the  theoretical 
study  of  the  frequencies  which  were  to  be  expected 
in  the  case  of  helium. 

In  the  Bohr  formulae  there  are  implicitly  contained 
a  large  number  of  statements  which  have  since  been 
checked.  His  expressions  for  hydrogen  and  helium 
show  the  entire  range  of  possible  frequencies.  The 
theory,  however,  has  been  extended  by  Sommerfeld 
who  endeavored  on  the  basis  of  an  ellipticity  in  some 
of  the  orbits  to  account  for  the  fact  that  the  charac- 
teristic lines  are  not  always  single2  as  would  be  re- 
quired by  the  simple  theory  of  circular  orbits. 

It  has  already  been  stated  that  three  series  of  char- 
acteristic lines  appear  in  the  X-ray  spectra  of  the 
elements  above  sodium  and  that  the  X-ray  spectra 
of  the  elements  below  sodium  have  not  yet  been  de- 
termined. On  the  basis  of  the  Bohr  theory,  which 
implicitly  includes  the  relation  determined  experi- 
mentally by  Moseley,  it  is  now  possible  to  assert  that 
the  Lyman,  Balmer,  and  Paschen  series  for  hydrogen 
are  the  K,  L  and  M  series  of  its  X-ray  spectrum. 
As  the  atomic  number  decreases,  the  frequency  of 
the  characteristic  X-ray  spectrum  also  decreases.  If 
this  relation  is  extended  by  extrapolation  to  hydro- 
gen it  gives  for  each  of  the  three  X-ray  series  the 

*0n  the  other  hand,  there  are  several  observable  phenomena 
which  have  not  been  amenable  to  treatment  on  the  Bohr  as- 
sumptions. The  Bohr  atom  is,  at  present,  largely  a  convenient 
assumption. 

2  It  has  also  been  suggested  by  A.  C.  Crehore  that  the  multi- 
plicity of  fine  lines  which  appear  in  spectra  is  due  to  the  nature 
of  the  paths  which  displaced  electrons  follow  in  their  return 
toward  the  nucleus. 


LIGHT  RADIATION  AND  ATOM-MODELS    163 

head  line  (highest  frequency)  in  one  of  the  three 
hydrogen  series. 

It  appears,  therefore,  that  the  mechanism  for  the 
production  of  light  is  fundamentally  the  same  as  that 
for  X-rays  and  that  the  only  difference  is  one  of  fre- 
quency. The  X-ray  spectra  are  merely  the  highest 
frequencies  for  atoms  of  large  atomic  number.  Be- 
low each  of  these  highest  frequencies  there  is  a  series 
of  terms  representing  frequencies  some  of  which  may 
not  be  visible  under  experimental  conditions. 

In  the  case  of  the  metals  the  spectra  which  are  ex- 
cited, when  an  electric  arc  is  formed  in  the  metallic 
vapor,  are  complicated  by  hundreds  of  lines.  An- 
alysis has  not  yet  been  accomplished  for  these  cases 
but  it  seems  safe  to  consider  that  the  lines  in  these 
arc-spectra  represent  lower  frequencies  in  series 
which  are  headed  by  the  characteristic  X-rays. 

Bohr's  formulae  implied  between  the  different 
series  of  X-ray  spectra  a  simple  relationship  which 
goes  far  to  indicate  the  fundamental  correctness  of 
his  assumptions.  The  relationship  was  verified  by 
reference  to  the  experimentally  determined  facts. 
In  the  K  series  which  is  shown  in  Fig.  26,  the  line  of 
longest  wave  length  (smallest  frequency)  is  desig- 
nated by  alpha,  and  the  next  by  beta,  after  the  con- 
ventional manner  for  all  spectral  series.  According 
to  Bohr's  theory  the  difference  in  frequency  between 
the  beta  and  the  alpha  lines  in  the  K  series  of  any 
element  should  be  the  frequency  of  the  alpha  line  of 
the  L  series. 

This  is  understandable  if  we  think  of  the  alpha  line 
in  the  K  series  as  due  to  jumping  from  orbit  2  of  Fig. 


164  WITHIN  THE  ATOM 

32,  to  orbit  1 ;  of  the  higher  frequency  beta  line,  with 
its  larger  quantum,  as  due  to  jumping  from  orbit  3 
to  orbit  1 ;  and  of  the  alpha  line  of  the  L  series  as  due 
to  jumping  from  orbit  3  to  orbit  2.  The  same  idea 
may  be  obtained  also  by  reference  to  the  arithmetical 
operations  of  page  158. 

The  permanent  configuration  which  is  reached 
when  an  electron  changes  in  orbit  is  always  one  in 
the  formation  of  which  the  maximum  amount  of 


FIG.  32 

Simplified  diagram  of  electronic  orbits  in  the  Bohr  atom-model. 

energy  is  emitted.  The  extreme  case  occurs  when 
an  isolated  electron  joins  a  nucleus  in  the  formation 
of  an  atom  or  neutralizes  the  negative  charge  pos- 
sessed by  an  atom  which  by  ionization  has  already 
lost  an  electron.  For  this  reason  radiation  of  line 
spectra  occurs  only  in  the  case  of  an  ionized  gas.  It 
does  not  accompany  the  process  of  ionization  which 
absorbs  energy  but  only  the  process  of  recombination 
when  this  energy  is  released. 

For  the  basic  ideas  involved  in  the  Bohr  atom- 
model  there  is  a  large  amount  of  evidence.     It  will 


LIGHT  RADIATION  AND  ATOM-MODELS    165 

be  noticed,  however,  that  it  does  not  conform  to  the 
picture  of  atom  structure  which  was  given  in  our 
early  chapters,  where  the  electrons  were  assumed  to 
occupy  relatively  fixed  positions  in  the  atom.  The 
concept  of  definitely  localized  electrons  is  highly 
satisfactory  to  the  chemists  who  have  found  it  to  ex- 
plain not  only  valence  in  chemical  combinations  but 
also  many  phenomena  like  the  miscibility  of  different 
liquids,  tendencies  to  vaporize,  and  hence  melting 
and  boiling  temperatures.  In  such  matters  mole- 
cules which  are  believed  to  have  like  shells  of  elec- 
trons are  found  to  have  similar  properties. 

Between  the  chemists  who  are  interested  in  molec- 
ular combinations  and  such  physicists  as  are  con- 
cerned with  radiation  there  is  at  present  established 
a  gulf.  Each  finds  his  own  atom-model  most  con- 
venient and  satisfactory.  The  chemical  model  is 
due  to  a  number  of  scientists,  chief  of  whom  are 
Lewis,  who  first  suggested  its  general  features,  and 
Langmuir,  who  has  elaborated  and  extended  it.  It 
requires  that  the  electrons  effective  in  valence  re- 
lations shall  be  relatively  fixed.  The  Bohr  atom  re- 
quires that  some,  at  least,  of  the  electrons  shall  be  in 
rotation. 

It  seems  quite  probable,  nevertheless,  and  indeed 
more  or  less  inevitable,  that  the  two  conditions  are 
not  hopelessly  conflicting  and  mutually  impossible. 
According  to  the  chemists'  construction  the  valence 
electrons  in  all  except  a  few  of  the  atoms  are  in  ex- 
ternal shells  within  which  are  other  shells  of  elec- 
trons. Perhaps  these  inner  shells  contain  the  ro- 
tating electrons  which  determine  the  radiation  of  the 


166  WITHIN  THE  ATOM 

ionized  atom.  In  the  case  of  the  elements  between 
lithium  and  argon,  however,  all  except  two  electrons 
are  in  a  single  shell.  It  is  possible,  therefore,  that 
future  investigations1  of  these  elements  will  lead  to 
evidence  upon  the  basis  of  which  a  reconciliation 
may  be  possible,  and  the  salient  features  of  both 
models  may  be  retained. 

That  the  electrons  of  an  atom  are  in  rotation  at 
least  while  light  is  being  radiated  is  well  proved  by 
other  phenomena  which  antedate  our  knowledge  of 
electrons.  Zeeman  in  1896  discovered  that  a  spec- 
tral line  which  originated  from  a  gaseous  source, 
placed  in  an  intense  magnetic  field,  appeared  as  three 
lines  when  the  magnetic  field  was  at  right  angles  to 
the  direction  of  the  propagation  of  the  light.  The 
central  line  had  the  original  position.  The  other 
two  lines  appeared  on  opposite  sides  of  the  original, 
one  representing  a  slight  increase  in  frequency  and 
the  other  a  corresponding  decrease. 

For  simplicity  of  discussion  let  us  imagine  the 
source  to  consist  of  only  three  atoms,  in  two  of  which 
the  electronic  orbits  are  coaxial  with  the  electronic 
streams  whose  motions  establish  the  magnetic  field. 
Suppose  the  directions  of  rotation  in  these  two  or- 
bits are  opposite.  Now  apply  to  these  rotating  elec- 
trons the  laws  stated  on  page  83  and  it  will  be  seen 

1  Characteristic  X-rays  are  produced  by  the  return  of  an  electron 
which  a  cathode  particle  has  knocked  out  of  its  normal  position 
in  an  atom.  Upon  assumptions  as  to  the  distribution  and  orbital 
conditions  of  the  electrons  in  an  atomic  system,  it  is  possible  to 
calculate  for  any  element  the  "critical  absorption"  frequency  for 
any  given  type  of  radiation,  e.g.,  the  K-type.  Calculations  were 
made  by  Duane  (1920)  upon  the  assumption  that  the  distribution 
of  electrons  was  that  of  the  Lewis-Langmuir  "static"  atom.  These 
agree  very  well  with  the  experimentally  observed  frequencies. 


LIGHT  RADIATION  AND  ATOM-MODELS     167 

that  one  is  urged  in  toward  the  center  of  its  orbit 
and  the  other  is  urged  out.  The  result  is  that  one 
acquires  a  slightly  larger  orbit  and  smaller  frequency 
while  the  other  acquires  a  smaller  orbit  and  higher 
frequency.  The  orbit  in  the  third  atom  we  assume 
to  be  in  a  plane  at  right  angles  to  the  orbits  of  the 
other  two  atoms  and  it  is  unaffected  by  the  magnetic 
field.  The  result  is  the  three  lines  described  above. 


CHAPTER  XIII 

MORE  EVIDENCE  FOR  THE  QUANTUM  HYPOTHESIS 

IN  preceding  chapters  there  have  been  mentioned 
two  types  of  emission  spectra,  line  and  continuous. 
Of  these  the  line  spectrum  is  the  more  interesting. 
It  is  emitted  by  elementary  substances  which  are  in 
the  state  of  a  gas  or  a  vapor,  when  the  electrons  have 
been  displaced  to  new  orbits  or  completely  detached 
from  the  atoms.  The  return  of  an  electron  is  ac- 
companied by  a  radiation  of  which  the  frequency  is 
characteristic  of  the  element  and  the  energy  equal 
to  one  quantum.  Line  spectra  are  due  to  the 
natural  vibrations  of  electrons  and  atomic  nuclei. 

A  continuous  spectrum,  on  the  other  hand,  is  a 
phenomenon  of  substances  in  the  solid  or  molten- 
liquid  state  where  the  atoms  are  packed  relatively 
close  together.  The  atomic  systems  no  longer  func- 
tion as  untrammelled  individuals  but  as  members  of 
a  large  and  unorganized  crowd.  Each  is  limited  in 
the  expression  of  its  tendencies  (line  spectrum)  by 
the  interrelations  and  reactions  with  the  other 
systems  of  its  milieu.  Energy,  imparted  to  the  atomic 
systems  under  these  conditions,  results  in  chaotic 
motions  on  the  part  of  all,  which  then  proceed 
to  jostle  and  crowd  each  other.  Instead  of  a  clear 
individual  expression,  which  is  characteristic  of  the 

168 


MORE  EVIDENCE  FOR  THE  QUANTUM    169 

atomic  type,  there  arises  a  roar  of  notes,  expressive 
only  of  conflict  and  chaos.  No  longer  are  types 
easily  distinguishable  by  characteristic  lines  for  the 
spectra  are  continuous.  Of  this  phenomenon  all  in- 
candescent solids  are  examples. 

When  the  disturbance  is  excited  by  impacts,  as  in 
the  case  of  "white"  X-rays,  the  highest  frequency 
which  is  radiated  is  determined  by  the  quantum  of 
energy  which  is  brought  to  the  radiating  substance 
by  an  impinging  electron.  A  quantum  relationship 
is  also  involved  in  radiations  of  lower  frequency. 

Under  the  conditions  where  a  continuous  spectrum 
is  produced  the  normal  oscillating  systems  of  nuclei 
and  planetary  electrons  are  altered  by  the  close 
presence  of  other  systems.  An  electron  is  no  longer 
concerned  only,  or  even  primarily,  with  its  natural 
oscillation,  for  the  electrons  of  each  atom  are  forced 
to  adapt  their  motions  to  the  external  influences. 
To  all  effects  and  purposes,  therefore,  the  radiating 
body  contains  at  any  instant  a  very  large  number  of 
oscillating  systems  which  differ  markedly  from  one 
another  in  form  of  vibration  and  in  frequency.  Mole- 
cules and  atoms,  as  well  as  the  intra-atomic  elements, 
enter  into  oscillation.  It  is  a  mad  dance,  in  which 
the  partners  are  changing  from  instant  to  instant, 
each  pair  dancing  to  its  own  tune.  Where  molecules 
and  atoms  are  vibrating,  frequencies  of  infra-red 
radiation  are  produced.  Where  an  electron  is  a  part- 
ner the  frequency  is  that  of  ultra-violet  light.  In 
the  visible  range  fast  vibrations  of  atoms  or  slow 
vibrations  of  electrons  are  presumably  the  cause  of 
the  radiation. 


170 


WITHIN  THE  ATOM 


When  we  speak  of  atoms  as  responsible  for  radia- 
tion we  do  not  mean  neutral  atoms,  but,  instead, 
those  which  are  electrically  charged  as  by  the  tem- 
porary loss  or  gain  of  an  electron.  That  such  atomic 
systems  exist  in  solids  we  have  seen  in  considering 
conduction  of  electricity  through  metals.  High  tem- 
perature, with  its  increased  molecular  agitation,  also 
favors  the  formation  of  such  atomic  oscillators. 


cm 


s  s 


FIG.  33 

Cross-section  of  a  uniform  temperature  enclosure,  showing  at  p 
a  peep-hole  for  studying  the  radiation  within.  A  circulation  of 
steam  maintains  the  temperature.  Screens  SS -shield  the  measur- 
ing instrument  /. 

Due  to  close  packing  of  molecules,  atoms,  and  elec- 
trons, any  solid  body  possesses  a  large  number  of  os- 
cillators of  different  electrical  and  geometrical  di- 
mensions and  hence  of  various  frequencies.  Such  a 
body,  therefore,  emits  or  absorbs  a  continuous  band 
of  frequencies.  The  emission  is  a  commonly  ob- 
servable phenomenon.  As  a  metal  body,  for  ex- 
ample, is  caused  to  rise  in  temperature  it  radiates 
heat  and  finally,  becoming  dull  red,  starts  to  radiate 
visibly.  As  the  temperature  is  still  further  increased 


MORE  EVIDENCE  FOR  THE  QUANTUM    171 

it  radiates  still  higher  frequencies,  becoming  incan- 
descent when  its  spectrum  includes  the  visible  range. 
The  absorption  phenomenon  is  not  so  easily  ob- 
served. Let  us  suppose,  however,  that  a  radiating 
body  is  placed  in  an  enclosure,  as  that  of  Fig.  33. 
Let  the  body  be  hi  equilibrium  with  the  walls  of  its 
enclosure,  that  is  with  its  surroundings,  receiving 
from  them  by  radiation  just  as  much  energy  as  it  in 
turn  is  radiating  to  them.  If  either  partner  in  this 
exchange  were  to  absorb  more  radiation  than  it  emit- 
ted its  temperature  would  rise.  The  assumed  con- 
dition, therefore,  is  one  of  temperature  equilibrium 
and  the  body  is  said  to  be  in  a  uniform  temperature 
enclosure. 

The  assumption  of  an  equality  of  exchange  means 
that  the  radiation  at  any  point  is  not  affected  by  the 
nature  of  the  body  or  its  surroundings,  nor  by  their 
relative  location.  For  example,  if  part  of  the  surface 
is  covered  with  lampblack  it  absorbs  nearly  all  of 
the  radiation  which  falls  upon  it,  but  it  must  radiate 
an  equal  amount  to  satisfy  the  condition  of  equilib- 
rium. Similarly,  if  part  of  the  surface  is  covered 
by  polished  metal  it  will  reflect  most  of  the  radiation 
and  hence  need  radiate  less  to  equal  what  it  absorbs. 
The  radiation  within  a  uniform  temperature  en- 
closure is  thus  everywhere  the  same. 

For  this  reason  it  is  impossible  by  the  radiation  to 
distinguish  one  part  from  another.  Within  a  cave 
all  objects  are  equally  black  unless  there  is  light  from 
an  entrance,  or  unless  the  condition  of  equilibrium 
is  violated  by  the  presence  of  a  torch,  which  is  an  ob- 
ject of  higher  temperature,  not  in  equilibrium  with 


172  WITHIN  THE  ATOM 

its  surroundings.  Similarly  if  one  looks  into  a  cru- 
cible or  into  a  large  furnace  when  conditions  are 
stable.  There  is  a  glare  of  light,  but  the  inner  sur- 
faces are  just  as  indistinguishable  as  are  those  of  the 
cave  where  the  temperature  is  lower. 

Within  a  uniform  temperature  enclosure  the  ra- 
diation is  altered  in  intensity  and  in  quality  only  as 
the  temperature  is  altered.  For  this  reason  such  ra- 
diation is  usually  called  "temperature  radiation." 
The  enclosure  itself  is  a  more  or  less  artificial  con- 
dition, an  ideal  or  limiting  case  of  equilibrium,  which 
has  been  adopted *  by  scientists  because  it  permits 
them  to  concentrate  their  attention  on  the  medium 
within  the  enclosure.  In  general,  bodies  ^are  not  in 
temperature  equilibrium  with  their  surroundings, 
and  particularly  not  when  these  include  a  human  ob- 
server. By  his  temperature  sense  he  is  frequently 
able  to  detect  a  lack  of  temperature  equilibrium  be- 
tween himself  and  his  surroundings. 

Two  important  laws  as  to  temperature  radiation 
have  been  known  for  many  years.  To  appreciate 
them  we  must  decide  upon  a  method  of  measuring 
temperature.  In  scientific  work  temperature  is 
measured  in  degrees  centigrade,  each  nine-fourths  of 
a  degree  Fahrenheit,  but  the  zero  is  the  so-called 
"absolute  zero." 

This  is  based  upon  a  phenomenon  of  gases.  When 
a  gas  is  heated  one  degree  it  is  found  that  the  hap- 
hazard molecular  motion  of  its  molecules  is  increased 
and  that  the  pressure  which  it  exerts  upon  the  walls 
of  its  container  is  also  increased  by  about  one-273rd 
part  of  the  pressure  which  this  same  volume  of  gas 


MORE  EVIDENCE  FOR  THE  QUANTUM    173 

would  exert  at  zero  degrees  centigrade  (32°  F.). 
Conversely,  if  it  is  cooled  by  an  equal  amount  there 
is  a  similar  reduction.  The  explanation  of  the  pres- 
sure is  found  in  the  impacts  of  the  molecules  on  the 
sides  of  the  container,  battering  it  like  a  steady  rain. 
The  effect  of  temperature  changes  is  explained  on 
the  basis  of  additions  of  kinetic  energy  to  the  mole- 
cules of  the  gas  or  of  subtractions  and  hence  of  corre- 
sponding alterations  in  their  average  speeds. 

Actual  gases  condense  into  liquids  and  freeze  into 
solid  form  at  low  temperatures  (and  under  high  pres- 
sures externally  applied).  The  scientist,  therefore, 
establishes  an  ideal  thermometer  by  using  an  ideal 
and  imaginary  gas  which  will  retain  throughout  all 
possible  ranges  of  temperature  the  characteristic 
which  actual  gases  like  hydrogen  show  at  ordinary 
atmospheric  temperatures.  Except  for  the  low  tem- 
peratures his  ideal  thermometer  is  identical  in  be- 
haviour with  an  actual  hydrogen  gas  thermometer. 
From  the  ideal  gas,  however,  he  may  imagine  the 
energy  to  be  successively  subtracted  until  the  kinetic 
energy  of  the  molecules  is  reduced  to  zero  and  the 
pressure  which  they  are  capable  of  exerting  is  also 
zero.  Since  each  degree  decrease  in  temperature,  be- 
low zero  on  the  centigrade  scale,  reduces  the  pressure 
by  1/273  of  its  value  at  zero  centigrade  it  will  only 
take  273  such  decreases  to  arrive  at  an  absolute  zero 
of  temperature.  On  this  thermodynamic  scale  of 
temperature  ordinary  room  temperature  is  obviously 
a  little  less  than  three  hundred  degrees. 

In  terms  of  absolute  temperatures  we  may  now 
express  two  important  empirical  laws  of  radiation. 


174 


WITHIN  THE  ATOM 


The  first  of  these  is  known  as  Wien's  law.  In  any 
temperature  radiation  there  is  some  frequency  which 
has  more  radiation  than  is  associated  with  any  other 
frequency.  This  frequency  becomes  greater  as  the 
temperature  is  made  higher;  and  it  is  directly  pro- 


"I€SO°C. 


1450  °C. 


I250°C. 


IOOO°C. 


-< Wave  Length 

-  Frequency >- 

FlG.  34 

Curves  showing  relation  of  intensity  of  radiation  and  frequency  of 
radiating  source  at  different  temperatures. 

portional  to  the  absolute  temperature.  There  is 
thus  a  displacement  of  the  frequency  of  maximum 
radiation  toward  the  ultra-violet  portion  of  the  con- 
tinuous spectrum  as  is  shown  graphically  hi  the 
curves  of  Fig.  34. 


MORE  EVIDENCE  FOR  THE  QUANTUM    175 

The  other  law,  due  to  Stefan  and  Boltzmann, 
states  that  the  total  radiation  from  a  heated  body 
varies  as  the  fourth  power  of  the  absolute  tempera- 
ture; thus  if  the  temperature  is  doubled  the  rate  at 
which  energy  is  emitted  is  increased  sixteen  times. 
It  is  also  illustrated  by  the  curves  of  Fig.  34. 

We  are  now  ready  to  consider  the  occasion  for 
Planck's  development  of  the  quantum  theory.  Up 
to  the  beginning  of  this  century,  when  he  made  his 
contribution  no  adequate  theory  had  been  developed 
to  explain,  or  to  picture,  the  experimental  relations. 
These  had  been  observed  by  careful  experiments  on 
enclosures  the  radiation  from  which  was  measured 
through  a  small  peephole  by  delicate  devices  sensi- 
tive to  heat. 

There  was,  however,  no  theory  on  the  basis  of 
which  formulae  could  be  logically  developed  which 
contained  the  relations  of  actual  experiment. 
Planck  solved  the  difficulty  by  reasoning  the  steps  of 
which  have  never  met  with  general  approval  but  the 
conclusions  of  which  are  firmly  established  in  the 
science  of  today. 

The  chief  difficulty  in  the  way  of  the  existing 
theories  concerned  the  manner  in  which  a  radiating 
body  shares  energy  with  its  ethereal  surroundings  or 
absorbs  it  from  them.  It  was  commonly  assumed 
that  energy  must  be,  or  rather  ought  to  be — for  the 
condition  was  contrary  to  fact — interchanged  in  a 
continuous  manner.  A  radiating  surface  was  recog- 
nized as  composed  of  a  number  of  oscillators,  but 
these  were  supposed  to  absorb  or  emit  continuously, 
that  is,  in  truly  infinitesimal  successive  amounts, 


176  WITHIN  THE  ATOM 

from  or  to  the  ether.  For  such  assumptions  there 
was  a  recognized  basis  in  theories  of  mechanics  and 
electrodynamics.  Of  this  a  mechanical  illustration 
may  be  quoted  from  Jeans. 

Suppose  we  construct  a  vibrating  system  by  con- 
necting a  number  of  corks  together  by  elastic  bands. 
Imagine  a  complicated  system,  if  you  will,  with  a 
large  number  of  cross  connections  between  various 
corks.  Now  disturb  this  by  pulling  some  of  the  corks 
from  their  equilibrium  positions  and  then  allow  the 
natural  oscillations  to  occur.  Let  this  system  with 
its  several  different  oscillations  be  placed  on  water. 
The  corks  simulate  a  vibrating  system.  The  water, 
with  its  almost  infinite  number  of  tiny  molecules, 
and  hence  infinite  possibilities  for  forms  of  vibration, 
simulates  the  ether.  We  know  what  happens. 
Equilibrium  between  these  two  systems  is  impossi- 
ble. The  energy  of  the  corks  is  all  absorbed  by  the 
water.  It  goes  into  vibrations  far  more  rapid  than 
those  of  the  corks,  for  it  goes  to  increase  the  motions 
of  the  invisible  molecules  of  the  water. 

If  the  ether  were  like  this  in  behaviour  all  the 
energy  of  the  bodies  in  a  temperature  enclosure 
would  be  abstracted  by  it.  And  the  energy  in  the 
ether  would  be  distributed  mostly  in  the  vibrations 
of  highest  frequency  instead  of  having  a  distribution 
with  a  definite  maximum  as  is  shown  in  Fig.  34. 

In  effect  Planck's  solution  of  the  difficulty  con- 
sisted in  postulating  a  condition  which  would  fit  the 
observed  phenomenon. 

To  an  economist  or  an  actuary  each  experimental 
curve  of  Fig.  34  looks  something  like  a  so-called 


MORE  EVIDENCE  FOR  THE  QUANTUM    177 

probability  curve,  such  a  curve,  for  example,  as  one 
would  plot  if  the  vertical  distances  represented 
numbers  of  men  and  the  horizontal  distances  repre- 
sented corresponding  lengths  of  life.  If  the  various 
oscillators  in  the  radiating  body  differ  in  their  abili- 
ties to  absorb  or  emit  radiant  energy,  each  being 
capable  of  only  a  definite  amount,  then  the  frequency 
of  maximum  radiation  should  depend  upon  the  char- 
acteristics of  these  oscillators  just  as  the  maximum  in 
a  plotted  curve  of  mortality  statistics  depends  upon 
the  characteristics  of  the  class  for  which  it  is  con- 
structed. To  a  very  large  extent,  as  we  shall  see, 
Planck's  theory  constituted  a  theory  of  probability 
for  electrical  oscillators. 

As  you  remember,  he  assumed  that  an  oscillator 
could  handle  only  a  quantum  of  energy;  and  by 
quantum  he  meant  an  amount  proportional  to  the 
frequency  of  vibration,  the  amount  hn.  Oscillators 
of  low  frequency,  even  if  relatively  numerous,  will 
handle  but  a  small  portion  of  the  total  energy  and 
contribute  but  little  because  the  amount  which  each 
individual  oscillator  may  handle  is  small.  On  the 
other  hand,  oscillators  of  large  frequency  will  respond 
only  if  there  is  available  a  relatively  large  amount  of 
energy  since  their  quanta  are  greater.  To  function, 
however,  the  higher  frequency  oscillator  must  re- 
ceive its  quantum  all  at  once;  it  cannot  make  it  up 
from  several  successive  smaller  quanta.  Since  large 
quanta  will  probably  occur  only  infrequently,  this  re- 
quirement means  that  there  will  be  little  total  energy 
associated  with  the  oscillators  of  high  frequency. 
The  maximum  radiation,  therefore,  will  occur  in  the 


178  WITHIN  THE  ATOM 

middle  range  of  frequencies,  as  the  experimental  re- 
sults indicate. 

Upon  the  assumption  of  quanta  Planck's  relations 
are  calculable  under  the  ordinary  laws  of  probability 
as  was  shown  by  Jeans  some  time  later.  For  pur- 
poses of  following  the  latter's  method  one  limits  his 
consideration  to  a  narrow  region  of  frequencies.  The 
quantum  will  be  essentially  the  same  for  all  the  fre- 
quencies within  this  narrow  band.  It  is  then  pos- 
sible to  calculate  the  probability  that  any  given  os- 
cillator of  this  frequency  will  have  zero  energy  or  the 
energy  of  one  quantum  or  that  of  two,  and  so  on. 
Summing  up  the  energy  which  a  large  number  of 
similar  oscillators  would  probably  have  at  this  fre- 
quency, Jeans  obtains  the  basic  expression  of 
Planck,  namely,  an  expression  for  the  probable 
average  energy  of  an  oscillator  at  any  desired  fre- 
quency. 

It  was  Einstein,  as  a  discrete,  or  indiscreet,  elec- 
tron remarked  between  chapters,  who  applied  this  re- 
lationship with  considerable  success  to  the  problem 
of  the  specific  heat  of  solids. 

Different  substances,  but  equal  quantities  by 
weight,  are  found  to  require  different  additions  of 
heat,  that  is  energy,  to  produce  equal  increases  in 
temperature.  The  amount  is  specific  to  each  sub- 
stance, and  hence,  the  term  "specific  heat"  is  applied 
to  the  amount  of  heat  required  to  change  by  one  de- 
gree the  temperature  of  unit  mass  of  a  given  sub- 
stance. The  common  unit  for  expressing  this  mag- 
nitude is  the  calorie  which  represents  approximately 
the  amount  of  energy  necessary  to  raise  one  gram  of 


MORE  EVIDENCE  FOR  THE  QUANTUM     179 

water  one  degree  Centigrade,  and  exactly,  that  re- 
quired for  the  degree  increase  in  temperature  be- 
tween 15  and  16  degrees  Centigrade. 

Temperature,  of  course,  is  a  numerical  answer  to 
the  question  "how  hot."  As  has  been  implied  above, 
it  measures  the  difference  in  hotness  of  substances 
the  molecules  of  which  differ  on  the  average  in  the 
kinetic  energy  which  is  associated  with  their  hap- 
hazard motions.  If  body  "A"  is  hotter  than  body 
"B,"  the  molecules  of  "A"  have,  on  the  average,  more 
kinetic  energy  than  those  of  "B".  It  is  for  this 
reason  that  a  hot  and  a  cold  body  when  placed  in 
contact  come  ultimately  to  a  common  temperature. 
By  molecular  collisions  at  the  contiguous  boundaries 
a  portion  of  the  energy  of  "A"  is  imparted  to  "B" 
until  finally  the  molecules  of  both  substances  have 
the  same  average  value  of  kinetic  energy. 

Because  of  differences  in  molecular  structure  one 
may  predict  at  once  that  different  substances  will 
have  different  specific  heats.  A  fairer  basis  of  com- 
parison, however,  than  amounts  of  heat  for  equal 
masses  would  be  the  amount  required  for  equal  num- 
bers of  molecules.  Molecules  of  similar  structure 
should  require  equal  amounts  of  energy  for  equal 
changes  in  temperature,  that  is,  they  should  have 
equal  "molecular  heats."  Thus  we  should  expect 
monatomic  molecules  to  be  alike  in  this  respect. 

In  a  monatomic  structure  the  mass  is  almost  en- 
tirely concentrated  in  the  nucleus,  which  is  the  center 
about  which  any  molecular  rotation  must  occur. 
From  the  familiar  example  of  flywheels,  we  know, 
however,  that  if  a  rotating  body  is  to  have  associated 


180  WITHIN  THE  ATOM 

with  it  large  amounts  of  energy,  the  mass  must  be 
separated  from  the  axis  of  rotation  by  a  large  dis- 
tance. Because  monatomic  molecules  are  not  con- 
structed on  the  plan  of  flywheels,  for  the  planetary 
electrons  are  negligible  in  mass  as  compared  to  the 
nucleus,  they  have  no  appreciable  energy  of  rotation. 
When  heat  is  added  to  monatomic  gases  it  all  goes  to 
increase  the  kinetic  energy  of  translation  of  the  mole- 
cules. 

A  diatomic  molecule,  however,  would  be  expected 
to  acquire  and  to  store  energy  in  a  rotation  or  spin- 
ning of  its  figure-eight-shaped  structure  and  particu- 
larly in  a  vibration  of  the  component  atoms  with  re- 
spect to  each  other.  In  the  haphazard  motion  of 
such  molecules  when  collision  occurs,  the  atomic 
partners  may  be  set  spinning,  or  they  may  momen- 
tarily be  crowded  together,  and  thus  vibrations  may 
be  set  up  within  the  molecular  system  itself.  It  ap- 
pears evident  that  collisions  will  lead  to  such  trans- 
fers of  energy,  and  hence  that  some  of  the  specific 
heat  of  diatomic  substances  will  represent  spinning 
and  vibratory  motions,  in  addition  to  the  haphazard 
translations  of  the  individual  molecules. 

The  molecular  specific  heat  of  a  substance  should, 
therefore,  depend  upon  the  molecular  structure, 
being  greater  "for  structures  which  have  greater 
variety  in  possible  types  of  motion — more  degrees  of 
freedom,  as  it  is  technically  said.  There  is  nothing, 
however,  to  indicate  that  the  molecular  specific  heat 
should  be  different  at  different  temperatures.  We 
should  expect  that  it  would  require  the  same  fraction 
of  a  calorie  to  change  a  substance  from  100  to  101 


MORE  EVIDENCE  FOR  THE  QUANTUM    181 

degrees  as  from  200  to  201  degrees.  Of  course,  if  a 
change  in  molecular  state  occurs  as,  for  example, 
from  liquid  to  vapor,  the  number  of  degrees  of  free- 
dom may  be  changed  and  we  may  be  dealing  in  effect 
with  a  different  substance.  As  long,  however,  as 
there  is  no  change  of  state,  it  would  appear  that  the 
specific  heat  of  any  substance  should  be  constant 
without  regard  to  temperature. 

For  monatomic  gases  it  is;  also  for  metals  in  a  va- 
por state;  but  for  all  other  substances  the  specific 
heats  are  found  to  be  markedly  decreased  as  the  tem- 
peratures at  which  they  are  measured  are  lowered. 
Here  again  no  adequate  theory  had  been  presented 
prior  to  the  application  of  the  quantum  hypothesis. 
The  theory  is  still  too  incomplete  to  account  for  any- 
where near  all  experimental  facts,  but  the  successes 
of  the  quantum  hypothesis  are  sufficient  to  indicate 
that  the  final  solution  must  involve  its  use. 

Planck  had  derived  an  expression  for  the  probable 
average  energy,  involving  a  large  number  of  similar 
oscillators.  This  Einstein  applied  to  the  study  of 
the  specific  heats  of  solids.  The  formula  is  too  com- 
plicated for  complete  discussion,  and  it  must  suffice 
to  say  that  it  involves  the  absolute  temperature  of 
the  substance.  A  mathematical  operation  was  then 
required  to  find  the  rate  at  which  this  energy  changed 
with  temperature,  that  is  to  find  the  specific  heat, 
which  is  the  change  in  energy  content  of  a  body  per 
degree  of  temperature.  The  expression  so  obtained 
was  in  form  to  permit  the  calculation  of  the  specific 
heat  of  solid  substances  at  any  desired  temperature 
if  the  frequency  of  the  oscillators  was  known. 


182 


WITHIN  THE  ATOM 


Several  methods  were  then  devised  by  Einstein 
and  others  for  obtaining  this  frequency  experi- 
mentally. Of  these,  only  one  will  be  discussed.  This 
depends  upon  a  number  of  principles  which  have  al- 
ready been  mentioned.  In  the  derivation  of  the  for- 
mula for  specific  heat  it  had  already  been  assumed, 
for  simplicity,  that  all  the  oscillators  of  a  homoge- 
neous body  were  essentially  alike.  It  remained  to 
excite  them  in  such  a  way  that  their  characteristic 
or  natural  oscillations  could  be  detected  and  their 


FIG.  35 

Cross-section  of  apparatus  for  studying  residual  rays.  Radiation 
from  a  source  T  is  successively  reflected  from  bodies  of  the  same 
substance.  The  residual  rays  are  analyzed  by  the  spectrometer, 
diagrammatically  indicated  at  L. 

frequency  measured.  You  will  remember  that  re- 
flection is  really  re-radiation.  Any  reflected  radia- 
tion must  then  include  most  prominently  those  ra- 
diations which  are  of  the  same  frequency  as  the  os- 
cillators would  themselves  naturally  emit.  The 
phenomenon  is  one  of  resonance,  so-called — that 
is  the  phenomenon  of  greatest  response  when  the  ap- 
peal strikes  the  proper  personal  note. 

If,  therefore,  a  substance  is  illuminated  by  a  con- 
tinuous spectrum  of  radiation,  such  as  would  arise 


MORE  EVIDENCE  FOR  THE  QUANTUM    183 

from  a  black  body  which  is  emitting  temperature 
radiation,  the  reflected  radiation  will  contain  more 
intensely  the  frequencies  natural  to  the  oscillators 
of  the  body.  Now  let  this  reflected  radiation  fall  on 
another  body  of  the  same  substance  as  the  first.  The 
general  scheme  is  illustrated  in  Fig.  35,  where  the 
progress  of  the  beam  of  radiation  is  indicated  by  the 
dotted  lines.  (A  mirror,  M,  is  interposed  at  one  point 
to  deflect  the  beam.)  At  the  second  reflecting  sur- 
face there  is  a  further  selection  of  the  natural  fre- 
quencies, and  a  further  discrimination  against  all 
others.  By  successive  reflections  there  are  thus  ob- 
tained so-called  "residual  rays,"  which  are  those 
natural  to  the  oscillators  under  examination. 

When  the  natural  frequency  is  known  the  calcula- 
tion of  specific  heat  by  Einstein's  method  may  be 
completed.  For  certain  substances  his  formula  was 
found  to  give  results  wonderfully  in  accord  with  the 
experimental  findings.  For  other  substances  there 
was  an  unsatisfactory  lack  of  agreement.  Neverthe- 
less, the  formula  agreed  in  such  cases  with  the  general 
trend  of  the  relations  between  specific  heat  and  tem- 
perature. It  indicated  a  certain  correctness  of  the 
general  method  of  approach  which  other  investi- 
gators have  been  rapidly  extending.  Thus  inquiry 
in  another  field  of  physical  science  was  stimulated 
and  is  being  advanced  by  the  fruitful  hypothesis  that 
energy  is  transferred  in  discrete  bundles,  the  magni- 
tudes of  which  are  dependent  only  on  the  frequencies 
of  the  atomic  and  electronic  oscillators  which  are 
concerned. 


CHAPTER  XIV 

ENERGY  AND  ITS  AVAILABILITY 

IN  the  earlier  chapters  of  this  book  the  orderly 
structure  of  matter  was  emphasized.  In  the  later 
chapters  some  evidence  was  presented  which  favors 
a  concept  of  "atomicity"  for  energy.  Throughout, 
it  is  to  be  hoped  that  the  text  has  conveyed  an  idea 
of  the  inherent  structural  order  of  nature.  Now  we 
must  distinguish  between  order  in  structure  and 
order  in  process.  The  processes  of  nature,  are  orderly 
only  in  the  sense  that  they  constitute  phases  of  an 
inevitable  sequence  of  events.  They  may  and  in- 
deed always  do  result  in  a  certain  disorder  which  we 
shall  now  consider.  Of  chaotic  conditions  we  have 
had  some  intimations  from  the  motions  of  molecules, 
particularly  those  of  gaseous  substances,  and  from 
the  electrical  elements  which  are  responsible  for  con- 
tinuous spectra. 

The  orderly  processes  of  nature  whereby  disorder 
results  have  been  formulated  in  a  law  commonly 
known  as  the  second  law  of  thermodynamics.  It 
would  be  preferable  to  speak  of  a  first  and  second  law 
of  energy  rather  than  of  thermodynamics,  but  they 
retain  the  titles,  descriptive  of  their  evolution,  for 
both  arose  at  a  time  when  the  relation  between  heat 
and  energy  was  inadequately  conceived.  Both  laws 

184 


ENERGY  AND  ITS  AVAILABILITY         185 

express  relations  which  have  been  grasped  more  or 
less  intuitively,  particularly  the  second  law. 

The  first  law  states  an  equivalence  between  work 
(energy)  and  heat;  and  in  mathematical  symbols  it 
contains  an  empirical  constant  for  converting  units 
of  heat  into  units  of  energy.  Prior  to  the  statement 
of  this  law  heat  and  mechanical  work  had  seemed 
unrelated  phenomena  and  different  units  had  been 
adopted  for  the  two  magnitudes.  Of  these  the 
calorie  has  already  been  defined ;  the  other  unit  is  the 
erg.  Whenever,  under  experimental  conditions 
energy,  associated  with  molar  bodies  disappeared, 
there  was  found  a  definite  increase  in  heat  which 
bore  the  proper  numerical  relationship  to  the  amount 
of  energy. 

For  many  years,  however,  it  has  been  recognized 
that  heat  is  merely  a  descriptive  term  for  the  kinetic 
energy  of  molecular  bodies.  Today  we  conceive  of 
energy  as  associated  with  all  electrons  and  protons, 
with  their  configurations  and  their  motions;  and  the 
first  law  becomes  our  statement  of  belief  in  the  con- 
servation or  indestructibility  of  the  entity  energy. 

The  second  law,  which  followed  the  work  of  Sadi 
Carnot  about  1824,  has  also  outgrown  its  earlier 
narrower  application  to  heat  engines  and  become  a 
general  law  of  energy.  At  various  times  it  has  re- 
ceived many  expressions,  of  which  the  most  service- 
able are  formulated  in  symbols  and  involve  a  con- 
cept known  as  entropy.  To  this  we  shall  return  in 
a  moment. 

In  so  far  as  the  second  law  is  a  matter  of  experi- 
ence it  records  the  impression  that  there  are  certain 


186  WITHIN  THE  ATOM 

natural  processes.  Water  flows  down  hill;  electric- 
ity moves  from  points  of  higher  to  points  of  lower 
potential;  by  radiation,  and  by  actual  molecular  im- 
pacts if  possible,  a  net  amount  of  energy  is  trans- 
ferred from  a  hot  to  a  cold  body;  impacts  of  molar 
bodies  and  all  phenomena  of  friction  result  in 
transfers  of  energy  to  molecules.  In  fact,  all  natural 
processes,  directly  or  ultimately,  result  in  greater 
kinetic  energy  on  the  part  of  molecules.  All  me- 
chanical operations  involve  friction  and  hence  all 
contribute  to  increase  the  kinetic  energy  of  molecular 
and  submolecular  systems.  Similarly,  the  con- 
duction of  electricity  and  many x  chemical  reactions 
result  in  greater  activity  on  the  part  of  the  tiny 
grains  of  our  physical  universe. 

Sometimes  the  second  law  is  stated  by  saying  that 
although  work  (the  expenditure  of  energy  in  con- 
nection with  molar  bodies)  may  always  be  converted 
into  a  definite  equivalent  of  heat  the  reverse  trans- 
formation is  always  incomplete.  This  was  the  earli- 
est expression  of  the  law  and  it  was  reached  by  a  con- 
sideration of  heat  engines.  Even  if  there  were  no 
friction  whatever,  a  heat  engine  could  never  be  100 
per  cent  efficient  unless  its  lowest  temperature  was 
zero  on  the  absolute  scale  of  temperature.  The  prop- 
osition was  originally  proved  by  Carnot,  who  dealt 
theoretically  with  an  ideal  engine  and  found  that  the 
efficiency  depended  upon  the  ratio  of  the  lowest  tem- 
perature, say  that  of  the  atmosphere,  to  the  highest 
temperature,  say  that  of  the  boiler.  The  efficiency 

1  When  we  consider  the  surroundings  as  well  as  the  reacting 
substances  all  reactions  result  in  increases  of  entropy. 


ENERGY  AND  ITS  AVAILABILITY         187 

is  always  less  than  100  per  cent  by  the  number  of  per 
cent  represented  by  this  ratio.  Since  temperatures 
are  measured  from  the  absolute  zero  it  is  evident  that 
all  actual  conversions  of  heat  into  work  are  remark- 
ably inefficient.  Of  the  mechanical  energy  derived 
from  heat  energy  there  is  always  a  certain  amount 
which  is  expended  in  friction,  so  that  the  actual  effi- 
ciency is  even  less  than  the  "thermodynainic  effi- 
ciency" which  has  just  been  explained. 

Energy  once  converted  into  heat  and  embodied  in 
molecular  motions  can  never  be  completely  recov- 
ered. Strictly  speaking,  therefore,  all  natural  proc- 
esses are  irreversible  because  things  can  never  be  as 
they  were.  The  fundamental  cause  of  this  so-called 
"thermodynainic  irreversibility"  is  to  be  found  in  the 
characteristics  of  molecular  systems. 

Any  material  systems  which  we  may  use  in  experi- 
mental investigations  involve  billions  and  billions  of 
molecules.  With  these  we  can. only  deal  statistically 
treating  of  average  effects.  Because  of  their  large 
number,  however,  the  desired  average  effects  may  be 
studied  by  the  laws  and  methods  of  probability,  the 
mathematical  science  of  chance. 

In  this  field  Maxwell  made  one  of  his  many  con- 
tributions to  science.  He  determined  the  distribu- 
tion of  velocities,  among  the  molecules  of  a  gas, 
which  would  satisfy  the  experimentally  observed 
condition  that  the  pressure  on  the  walls  of  a  retain- 
ing vessel  is  constant  when  the  temperature  is  con- 
stant. He  found  that  no  matter  how  collisions  oc- 
curred there  would  be  a  definite  average  velocity 
(perpendicular  to  the  surface  of  the  container)  and 


188  WITHIN  THE  ATOM 

that  the  proportion  of  the  total  number  of  molecules 
which  had  any  particular  velocity,  either  greater  or 
less  than  the  average,  was  definite  and  calculable. 
If  a  plot  is  made,  showing  the  percentage  of  mole- 
cules striking  the  container  and  their  corresponding 
velocities,  the  result  is  the  form  of  probability  curve 
shown  in  Fig.  36. 

We  have  already  met  one  application  of  the  theory 
of  probability  in  the  development  of  an  expression 
for  the  average  energy  of  a  large  number  of  oscil- 
lators, each  restricted  according  to  the  quantum  hy- 
pothesis. 


Velocity 
FIG.  36 

Diagrammatic  representation  of  Maxwell's  distribution  of  molec- 
ular velocities. 

We  shall  now  sketch  briefly  an  application  of  the 
method  of  probabilities  by  which  Boltzmann  arrived 
at  a  concept  of  entropy,  the  characteristic  magnitude 
in  terms  of  which  the  second  law  is  most  satisfac- 
torily expressed.  Imagine  looking  across  two  paral- 
lel tennis  courts.  The  players  are  warming  up  for 
two  sets  of  doubles  and  each  member  of  a  team  is 
volleying  with  an  opponent  so  that  four  balls  are 
constantly  in  the  air.  We  shall  distinguish  between 
the  balls  by  the  letters  a,  b,  c,  and  d. 

The  distribution  of  the  balls  with  reference  to  the 
line  of  the  nets  changes  from  instant  to  instant.  At 
one  moment  all  four  may  be  on  the  east  side,  and  a 


ENERGY  AND  ITS  AVAILABILITY         189 

moment  later  three  on  that  side  and  one  on  the  west. 
There  are  obviously  five  possible  distributions, 
namely :  all  east,  all  west,  three  east  and  one  west,  or 
vice  versa,  and  two  on  each  side  of  the  net. 

For  any  distribution  there  is  one  or  more  "com- 
plexions," as  they  are  called.  Thus  the  distribution 
of  three  east  and  one  west  might  be  the  result  and 
would  correspond  to  any  one  of  four  complexions, 
for  there  are  four  different  ways  in  which  we  may 
have  three  balls  on  one  side  and  one  on  the  other. 
If  we  tabulate  the  various  possible  complexions  we 
have  the  result  given  below : 


Distribution                                           Complexion 
East        West                                        East        West 
4              0                                            abed 

3               i                                                abc 
abd 
acd 
bed 

d 
c 

b 

a 

22                                                 ab 
ac 
ad 
be 
bd 
cd 

cd 
bd 
be 
ad 
ac 
ab 

i               3                                                   a 
b 
c 
d 

bed 
acd 
abd 
abc 

o  4  abed 

The  distribution  of  two  balls  on  either  side  of  the 
net  is  the  most  probable  distribution.    Out  of  six- 


190  WITHIN  THE  ATOM 

teen  possible  complexions  this  distribution  contains 
six,  and  that  with  the  next  largest  number  contains 
four.  For  purposes  of  later  analogy  we  also  note 
that  this  distribution  of  two  and  two  represents  a 
sort  of  an  equilibrium  condition.  We  might  also 
note  that  from  the  standpoint  of  an  attendant,  who 
is  accustomed  to  seeing  balls  neatly  packed  in  dozens, 
the  distribution  is  not  that  of  order. 

Now  forget  the  players,  letting  the  balls  represent 
molecules  of  a  gas  and  let  their  number  be  enormous- 
ly increased.  There  will  still  be  a  distribution  which 
will  contain  the  maximum  number  of  complexions 
and  this  will  be  the  most  probable  distribution.  It 
will  also  be  the  most  probable  state  for  the  gas,  the 
final  "equilibrium  state"  toward  which  systems  of 
gas  molecules  inevitably  tend.  It  will  be  the  state 
with  the  largest  number  of  complexions  and  the 
greatest  number  of  ways  in  which  the  gas  molecules 
may  be  associated,  the  state  of  greatest  disorder. 

As  Boltzmann  defined  it,  "thermodynamic  prob- 
ability" is  a  number  which  expresses  how  much  more 
probable  a  given  state  is  than  some  "standard"  or 
perfectly  ordered  state  in  which  the  substance  occu- 
pies the  same  volume  and  has  the  same  energy. 
For  example,  from  the  preceding  table  we  see  that 
the  probability  of  the  most  "mixed-up"  state  is  six 
times  that  of  the  state  where  all  the  balls  are  on  one 
side  of  the  net.  The  mixed-up  state  is  most  prob- 
able. There  is  always  a  natural  trend  toward  the 
greatest  disorder,  toward  the  state  of  final  equilib- 
rium. 

When  four  balls  are  on  one  side  of  the  net  there  is 


ENERGY  AND  ITS  AVAILABILITY         191 

greater  energy  associated  with  this  side  than  with  the 
other.  Hence,  if  we  were  dealing  with  molecules  we 
would  expect  to  obtain  some  of  this  energy  by  allow- 
ing them  to  pursue  their  natural  haphazard  motions 
and  by  their  impacts  to  drive  before  them  a  molar 
body  like  the  piston  of  an  engine.  Haphazard  mo- 
tions will  carry  the  balls  across  the  net  and  they  can 
do  mechanical  work,  as,  for  example,  upon  a  racquet 
held  in  their  way.  In  the  equilibrium  state,  how- 
ever, no  mechanical  work  can  be  recovered,  for  on  the 
average  a  racquet  held  over  the  net  would  receive  as 
many  and  as  hard  impacts  from  one  side  as  from  the 
other.  We  now  see  that  we  cannot  utilize  or  obtain 
from  a  gas,  in  the  state  analogous  to  four  balls  on 
one  side,  all  the  energy  which  its  molecules  appear  to 
be  able  to  expend,  since  the  natural  process  upon 
which  we  rely  proceeds  only  to  a  final  equilibrium 
state  corresponding  to  that  of  two  balls  on  either  side 
of  the  net. 

Unfortunately  for  the  purposes  of  easy  exposition, 
thermodynamic  probability  and  entropy  are  not 
synonymous.  There  is,  however,  a  definite  relation 
between  them.  If  one  increases  the  other  also  in- 
creases but  not  in  direct  proportion.  With  this 
understanding  we  may  proceed  to  use  the  term  en- 
tropy in  place  of  thermodynamic  probability. 

All  systems  tend  to  a  final  state  of  maximum  en- 
tropy, that  is  a  condition  of  greatest  molecular  dis- 
order from  which  no  mechanical  work  may  be  de- 
rived. Not  only  no  mechanical  work  but  also  no 
chemical  or  electrical  changes  can  be  brought  about 
by  such  a  system  of  itself  in  such  a  manner  as  to  per- 


192  WITHIN  THE  ATOM 

mit  energy  to  be  derived  from  these  changes.  The 
equilibrium  condition  is  a  "run-down  condition" 
which  offers  no  hope  to  human  beings  who  would 
control  ni*4ure's  store  of  energy.  Although  energy  is 
still  associated  with  the  system  its  availability  has 
disappeared. 

Human  beings  need  never  be  concerned  with  the 
conservation  of  energy  since  that  is  apparently  in- 
herent in  the  entity  itself.  Their  concern  is  with  its 
availability.  When  energy  transformations  occur 
naturally,  and  in  final  analysis  all  transformations  so 
occur,  there  is  a  reduction  in  availability,  or  as  the 
scientist  says,  an  increase  in  entropy.  There  is  no 
known  or  anticipated  scientific  process,  despite  all 
the  discoveries  of  radioactive  substances,  whereby 
this  inevitable  and  natural  increase  in  entropy  may 
be  avoided.  It  does  seem  unnecessary,  however, 
that  man  should  accelerate  the  irreversible  trans- 
formations of  nature.  This  he  does  whenever  he 
fails  to  take  from  a  natural  process,  as,  for  example, 
from  the  combustion  of  coal,  the  full  amount  of  use- 
ful energy  which  is  his  equity  in  accordance  with  the 
second  law  of  thermodynamics. 

The  final  end  of  any  conservative  system,  one 
which  does  not  have  energy  communications  with  its 
neighbors,  is  not  stagnation  but  disorder.  Orderly 
systems  may  have  no  more  energy  than  disorderly 
systems  but  their  energy  is  partly  available.  In- 
evitably any  orderly  system  tends  to  a  state  of  maxi- 
mum disorder.  In  the  process  of  attaining  this  state 
its  own  entropy  is  increased.  Only  a  certain  amount 
of  its  energy  is  available  and  the  expenditure  of  this 


ENERGY  AND  ITS  AVAILABILITY          193 

margin  is  man's  concern.  It  may  be  expended  with 
foresight,  as  when  a  waterfall  is  utilized  to  make 
chemical  compounds  in  which  available  energy  is 
stored  for  later  release,  for  example,  in  -nitrogenous 
fertilizers.  It  may  be  expended  without  foresight  in 
the  innumerable  ways  which  history  records.  Every 
fire  or  explosion,  every  inefficient  process,  represents 
an  increase  in  the  world's  entropy — the  sum  total  of 
its  disorder. 


APPENDIX 

THE  MAGNITUDES  OF  ELECTRONS  AND  QUANTA 

To  a  considerable  extent  the  exposition  of  the 
previous  text  has  been  unrelated  to  our  daily  experi- 
ences. It  has  dealt  with  minute  protons  and  elec- 
trons, with  quanta  of  energy,  and  with  granular 
structures  so  fine  that  they  are  only  to  be  inferred 
and  never  to  be  seen.  In  this  Appendix  it  is  now 
proposed  to  assemble  some  numerical  expressions 
whereby  the  tiny  magnitudes  involved  in  the  modern 
science  of  electrons  and  quanta  may  be  related  to  the 
grosser  magnitudes  with  which  we  are  familiar. 

In  terms  of  the  fundamental  scientific  units, 
namely,  the  centimeter  (1  cm.— 0.394  inch),  the 
gram  (1  g.=0.0353  ounce),  and  the  second,  the  sizes 
and  masses  of  the  electrical  elements  are  extremely 
small  and  their  number  in  any  sensible  volume  ex- 
tremely large.  Where  extremes  are  to  be  met, 
numerical  expression  is  most  conveniently  accom- 
plished by  a  slight  modification  of  our  common 
decimal  system. 

Consider  first  the  expression  of  numbers  greater 
than  ten.  Ten  is  one  times  ten;  a  hundred  is  one 
times  ten  times  ten;  and  one  thousand  is  one  times 
the  successive  product  of  three  tens;  and  so  on  as  in 

195 


196  WITHIN  THE  ATOM 

the  table  below.  The  number  of  successive  products 
of  ten  are  represented  by  exponents  of  the  proper 
value  as  shown. 

io  —  i  X  io  =  i  x  io1 

loo  =  i  X  io  X  io  =  i  x  io2 

1000=  i  X  io  X  io  X  io  =  i  X  io3 

10000=1  X  io  X  io  X  io  X  10=  i  X  io* 

one  million  =  —  i  X  io6 

one  billion  =  =  i  X  io9 

one  million  million  =  =  i  X  io12 

one  billion  billion  =  —  i  X  io18 

On  the  same  basis,  any  number  like  606  is  6.06 
times  a  hundred  or  as  illustrated  below : 

606  =  6.06  X  io2 

6060  =  6.06  X  io3 

60600  =  6.06  X  10* 

When  later  we  find  that  the  number  of  molecules 
in  two  grams  of  hydrogen  gas  is  6.06X10  23  we  shall 
be  able  to  convert  this  expression  into  606  thousand 
billion  billion,  and  thus,  perhaps,  get  some  apprecia- 
tion of  an  enormous  number. 

For  numbers  smaller  than  unity  the  system  is 
equally  simple.  We  write  1/10  as  IO"1;  and  1/100 
as  1/102  and  then  as  1X10"2,  as  in  the  following 
table: 

o.i     =  i  X  i/io    =    X  io-1 
o.oi    =  i  X  i/ loo  = 
o.ooi  =  i  X  i/io3    = 
one  millionth  =  = 

one  billionth  =  = 

one  billionth  of  a  billionth  = 


X 
X 
X 
X  io- 


18 


MAGNITUDES  OF  ELECTRONS  AND  QUANTA  197 

The  use  of  these  negative  powers  of  ten  is  illustrated 

below: 

0.254  =  2.54  X  1/10  =  2.54  X  10'1 
0.0254  =  2.54  X  10'2 

0.00254         =  2.54  X  10'8 
0.000,002,54  ==  2.54  X  10'6 

In  addition  to  the  convenience  and  brevity  which 
this  system  offers  it  serves  to  indicate  most  quickly 
the  order  of  magnitude  of  a  number  and  its  signifi- 
cant figures.  Consider  for  example  the  value  of  Avo- 
gadro's  constant,  that  is  the  number  of  molecules  in 
one  "mole"  of  any  substance. * 

The  most  exact  value  for  this  constant  is  6.062  X 
1023,  as  found  by  Millikan. 

From  the  second  portion  of  this  expression  we 
recognize  at  once  that  the  constant  is  of  the  order  of 
hundreds  of  thousands  of  a  billion  billions.  The 
first  portion  of  the  number  contains  the  significant 
figures.  If  Millikan's  determination  had  been  less 
precise  he  might  have  found  6.06 XlO23,  or  with  still 
less  accuracy  6.0  XlO23.  In  the  latter  case  he  would 
not  have  written  the  number  as  6.000X1023  for  that 
would  have  implied  the  same  precision  as  does  his 
actual  value,  that  is  a  precision  to  the  fourth  signifi- 
cant figure. 

By  the  number  of  significant  figures  an  experi- 
menter indicates  the  correctness  of  his  results  so  far 
as  concerns  the  precision  with  which  he  has  made  his 
measurements.  He  does  not,  of  course,  mean  that 

*A  mole  is  a  number  of  grams  equal  to  the  molecular  weight 
of  the  substance ;  thus  in  the  case  of  hydrogen,  H2,  a  mole  is  two 
grams,  but  in  that  of  oxygen,  0>,  it  is  32  grams.  Without  regard 
to  substance  all  moles  will  contain  the  same  number  of  molecules. 


198  WITHIN  THE  ATOM 

there  may  not  be  present  in  his  determination 
sources  of  error,  inherent  in  the  experimental  con- 
ditions, which  may  have  rendered  his  results  wrong 
even  in  order  of  magnitude.  By  proper  attention  to 
significant  figures  throughout  any  necessary  calcula- 
tions he  arrives  at  a  final  result  each  figure  of  which 
is  really  significant  and  not  merely  a  result  of  an 
arithmetical  process. 

Taking  a  simple  example,  suppose  he  wishes  to 
compute  the  circumference  of  a  circle  the  diameter 
of  which  he  has  measured  as  10.0  cm.  He  multiplies 
this  diameter  by  Jt,  but  he  uses  for  n,  3.14  and 
not  3.14156  or  some  still  more  accurate  value.  By 
his  expression  of  the  diameter  as  10.0  cm.  he  means 
in  substance  that  he  has  measured  it  with  a  centi- 
meter scale  which  is  divided  into  tenths  of  a  centi- 
meter, and  that  he  does  not  know  its  value  closer 
than  a  tenth  of  a  centimeter.  To  write  the  circum- 
ference as  31.4156  cm.  would  imply  a  greater  accur- 
acy than  he  has  either  right  or  desire  to  imply. 

When,  therefore,  we  consider  Millikan's  value  for 
Avogadro's  constant  we  interpret  it  to  mean  that  he 
has  determined  the  number  of  molecules  in  a  mole 
to  the  fourth  significant  figure.  His  value,  then  is 
in  doubt  by  approximately  0.001  XlO23  or  a  mere 
matter  of  a  hundred  or  so  billion  billion  molecules. 
He  is  right,  however,  to  within  about  one-hundredth 
of  one  per  cent.  A  more  exact  knowledge  than  this 
would  probably  avail  us  but  little  since  there  are  few 
physical  conditions  where  we  may  detect  a  percent- 
age difference  as  small  as  this,  and  few  physical  con- 


MAGNITUDES  OF  ELECTRONS  AND  QUANTA  199 

stants  which  are  expressible  by  more  than  four  sig- 
nificant figures. 

We  are  now  in  a  position  to  express  numerically 
some  important  physical  magnitudes.  We  shall 
not,  however,  go  into  any  detail  as  to  how  they  have 
been  determined.  Further,  we  shall  allow  the 
numerical  values  to  create  their  own  impressions 
instead  of  adopting  conventional  expedients  to 
heighten  them.  For  example,  one  might  count  the 
average  number  of  letters  on  a  page  of  the  encyclo- 
paedia, divide  this  number  into  Avogadro's  constant 
and  find  the  number  of  pages  which  would  be  re- 
quired to  contain  a  number  of  letters  equivalent  to 
this  number  of  molecules,  and  then  calculate  the 
number  of  billions  of  complete  sets 1  and  so  convey 
an  impression.  With  more  tediousness  he  could  take 
the  volume  of  atmospheric  gas  inspirated  by  an  av- 
erage man  in  a  single  breath  and  by  using  Avogadro's 
constant  express  the  number  of  molecules  for  this 
familiar  case  in  terms  of  volumes  of  the  encyclo- 
paedia. Arithmetical  dexterity  and  interest  will 
produce  strange  results  by  such  a  method,  and  the 
arithmetic  is  facilitated  by  the  use  of  powers  of  ten. 

Sizes :  Known  distances  in  the  physical  universe 
extend  from  1024  cm.,  representing  the  distance  from 
the  earth  to  the  further  nebulae,  to  10'13,  representing 
the  order  of  magnitude  of  the  diameter  of  an  elec- 
tron. With  the  microscope  one  can  observe  dis- 
tances in  ordinary  light  of  the  order  of  10'5  cm.,  and 
can  detect  illuminated  specks  of  somewhat  smaller 

1  The  advertisements  say  4.4  x  108  words  per  set.  Hence,  allow- 
ing six  letters  to  the  word,  almost  a  billion  billion  sets. 


200  WITHIN  THE  ATOM 

dimensions.  The  diameter  of  a  molecule  of  oxygen 
is  2.99  X 10'8  cm.  For  hydrogen  the  diameter  is  less, 
being  2.17X10'8  cm.  The  best  indications  of  the 
diameter  of  an  electron  give  2X10'13  cm. 

Masses:  The  mass  of  a  hydrogen  molecule  is  3.33 
XlO'24  g.,  and  the  mass  of  any  other  molecule  is 
larger  in  proportion  to  its  molecular  weight,  thus 
that  of  the  oxygen  molecule  is  52.8  XlO'24  g.  The 
mass  of  the  atom  of  hydrogen  is  half  that  of  its  mole- 
tule  and  this  is  also  the  mass  of  the  proton.  The 
mass  of  an  electron  is  only  about  1/1845  of  the  pro- 
ton and  is  thus  9.01  X10'28  g. 

Velocities:  The  greatest  velocity  in  the  physical 
universe  is  that  of  light  or  of  other  forms  of  radiant 
energy.  Light  quanta  apparently  travel  2.999  X 
1010  cm.  per  second.  Beta  particles  have  been 
measured  with  velocities  as  high  as  9/10  of  this. 
Alpha  particles,  with  their  greater  mass,  are  ejected 
with  smaller  velocities  in  the  order  of  1/10  the 
velocity  of  light. 

In  a  volume  of  gas  under  practically  atmospheric 
conditions  of  pressure  and  temperature  (so-called 
standard  conditions)  molecules  travel  with  velocities 
which  are  dependent  upon  their  masses.  Hydrogen 
molecules  travel  fastest,  about  a  mile  a  second  or 
1.69 XlO5  cm.  per  second.  Oxygen  molecules  with 
sixteen  times  the  mass  travel  one-quarter  as  fast  as 
hydrogen  molecules,  that  is  4.2X104  cm.  per  second. 

Free  Path  of  Gas  Molecules:  Under  these  stand- 
ard conditions  the  atoms  of  a  volume  of  hydrogen 
would  travel  on  the  average  about  1.76 XlO'5  cm.  be- 
tween successive  collisions.  On  the  average,  there- 


MAGNITUDES  OF  ELECTRONS  AND  QUANTA:  201 

fore,  a  hydrogen  atom  would  make  ten  billion  col- 
lisions per  second.  If  the  gas  is  less  dense,  for  ex- 
ample, if  the  container  has  been  exhausted  until  the 
pressure  is  2.64  X10"10  of  the  normal  atmospheric 
pressure,  the  number  of  molecules  per  c.c.  has  been 
similarly  reduced  and  the  mean  free  path  is  increased 
by  3.8  XlO9  times.  For  oxygen,  for  example,  the 
mean  free  path  under  atmospheric  conditions  is  9.4 
XlO"4  cm.  and  under  the  above  conditions  of  rare- 
faction 3.54 XlO4  cm. 

The  velocity  has  not  been  altered  by  the  reduction 
in  pressure  for  the  temperature  has  been  assumed 
unchanged,  and  hence  the  kinetic  energy  is  not  al- 
tered. The  molecule  will  now  make  only  about  one 
collision  a  second.  Such  extreme  conditions  of  rare- 
faction are  producible  today  by  vacuum  pumps 
which  employ  molecules  to  bombard  other  molecules 
and  thus  drive  them  from  the  desired  enclosure. 
When  the  bombarding  molecules  have  done  their 
work  they  are  removed  by  condensing  them  into 
drops  of  liquid. 

Avagadro's  Constant:  A  mole  of  any  gas  occu- 
pies a  volume  of  2.241  XlO4  c.c.,  that  is,  about  22 
liters  (about  0.79  cubic  foot)  under  standard  con- 
ditions of  temperature  and  pressure.  In  this  mole 
there  are,  as  has  been  said,  6.062 XlO23  molecules. 
Per  cubic  centimeter,  therefore,  there  are  about  2.705 
XlO19  molecules.  Under  the  conditions  of  rare- 
faction which  were  mentioned  above  as  attainable  by 
the  modern  mercury  vapor  vacuum  pump  the  num- 
ber per  c.c.  is  reduced  to  about  7 XlO9,  so  that  the 
nearest  we  can  come  to  a  perfect  vacuum  is  a  mere 


202  WITHIN  THE  ATOM 

matter  of  several  billion  molecules  in  each  cubic 
centimeter. 

Energy  Units :  The  unit  of  energy  is  the  erg.  It 
represents  twice  the  kinetic  energy  which  is  asso- 
ciated with  a  mass  of  one  gram  which  is  moving  at 
the  rate  of  one  centimeter  a  second.  It  represents 
roughly  one- thousandth  of  the  work  required  to  raise 
a  gram  vertically  one  centimeter.  It  is  too  small  a 
unit  for  convenience  in  practical  mechanics.  For 
example,  in  lifting  an  ounce  vertically  a  distance  of 
1-inch  one  does  7.07  X 104  ergs  of  work.  The  familiar 
unit  of  energy,  known  as  the  foot-pound,  is  equiva- 
lent to  1.35X107  ergs.  The  joule  which  is  used  in 
electrical  engineering  is  107  ergs.  The  calorie  which 
is  the  convenient  unit  for  measuring  energy  which 
appears  as  heat  is  equivalent  to  4.19X107  ergs. 

Quanta:  Although  the  erg  is  too  small  for  many 
practical  purposes  it  is  large  compared  to  many  of 
the  amounts  of  energy  with  which  the  scientist  is 
concerned.  This  is  particularly  so  in  the  case  of 
quanta.  Planck's  constant  is  6.56X10'27  and  the 
number  of  ergs  representing  a  quantum  at  any  given 
frequency  is  the  product  of  this  constant,  h,  and  the 
frequency  n.  For  example,  about  the  highest  fre- 
quency of  visible  light  is  7.5  XlO14  vibrations  per 
second,  so  that  the  corresponding  quantum  is  5.0  X 
10"12  erg.  The  frequency  at  which  a  heated  body 
radiates  the  maximum  amount  of  energy  is  about 
1.5X  1014,  which  is  in  the  infra-red  region.  The  cor- 
responding quantum  is  only  9.9 XlO"13  erg. 

Gamma  rays  have  the  highest  known  frequencies, 
about  1020  vibrations  per  second.  In  this  case  the 


MAGNITUDES  OF  ELECTRONS  AND  QUANTA  203 

quantum  has  its  maximum  known  value  of  about  6 
XlO-7  erg. 

Kinetic  Energy  of  a  Gas  Molecule:  The  kinetic 
energy  which,  on  the  average,  is  associated  with  each 
molecule  of  a  gas  under  standard  conditions  of  pres- 
sure and  temperature  (0°C.)  is  5.62X10"14  erg,  and 
for  every  degree  increase  in  temperature  the  kinetic 
energy  of  translation  is  increased  by  2.06  XlO'16  erg. 

Electrical  Units:  For  measuring  electrical  phe- 
nomena three  systems  of  units  are  used,  but  we  shall 
restrict  ourselves  to  the  so-called  practical  units 
known  to  electricians  and  the  consumers  of  electrical 
energy. 

The  Electron:  The  practical  unit  of  quantity  of 
electricity  is  the  coulomb.  It  represents  the  amount 
of  electricity  which  would  be  transferred  in  a  silver- 
plating  solution  of  silver  nitrate  every  time  that 
0.001118  gram  of  silver  is  deposited  on  the  cath- 
ode. If  a  coulomb  is  passed  through  an  electrolyte 
under  conditions  where  hydrogen  is  liberated  the 
mass  of  hydrogen  gas  is  1.038X  10"5  gram.  To  liber- 
ate a  gram  of  hydrogen  requires  the  passage  of  96,- 
500  coulombs.  In  terms  of  the  coulomb  the  charge 
of  an  electron  (or  of  a  proton)  is  1.591  XlO"19  coul- 
omb. 

Current:  When  there  is  a  transfer  of  electricity 
through  any  conductor  at  the  rate  of  one  coulomb 
per  second  a  current  of  one  ampere  is  said  to  be  flow- 
ing. It  is  thus  evident  that  a  current  of  one  ampere 
represents  a  flow  across  each  and  every  cross-section 
of  the  conductor  of  6.3 XlO18  electrons  each  second. 

Electrical  Potential:     When  a  coulomb  of  elec- 


204  WITHIN  THE  ATOM 

tricity  is  transferred  between  two  points  by  an  ex- 
penditure of  one  joule  of  energy  (107  ergs)  the  points 
are  said  to  differ  in  electrical  potential  by  one  volt. 
The  lighting  circuit  of  a  house  or  office  usually  oper- 
ates at  a  voltage  of  115. 

Power:  By  multiplying  the  voltage  across  and 
the  current  through  any  piece  of  electrical  apparatus 
we  find  the  number  of  joules  per  second  which  are 
being  expended  in  the  apparatus.  For  joules  per 
second,  however,  there  is  used  a  single  word,  namely, 
watts.  When  energy  is  being  expended  at  the  rate 
of  one  joule  per  second  the  power  in  the  circuit  is 
one  watt.  An  ordinary  house  light,  rated  as  40 
watts,  takes  a  current  of  40/115  ampere  or  a  little 
more  than  a  third  of  an  ampere,  and  represents  a 
flow  of  electrons  at  the  rate  of  about  2.X1018  a 
second. 

lonization  Potential:  The  kinetic  energy  which 
an  electron  acquires  in  free  passage  between  two 
points  differing  in  potential  by  one  volt  is  about  1.59 
XlO'11  erg.  lonization  potentials  are  of  the  order 
of  10  volts  so  that  it  requires  about  1.6X10"10  erg  to 
knock  an  electron  free  from  an  atomic  structure. 
The  ionization  potential  differs  with  the  type  of 
atom  and  some  atoms  require  two  or  three  tunes  as 
much  energy  in  the  impact  as  do  others.  To  ionize 
by  removing  two  electrons  requires  more  energy  but 
the  amount  is  still  absurdly  small  compared  to  any 
of  the  energy  expenditures  of  our  daily  lives. 

X  rays :  In  an  X-ray  tube  the  electrons  freed  at 
the  heated  cathode  are  pulled  across  the  intervening 


MAGNITUDES  OF  ELECTRONS  AND  QUANTA  205 

space  to  the  target  under  voltages  of  the  order  of 
150,000.  As  a  result  each  electron  delivers  to  the 
target  an  energy  of  about  2.4  XlO'6  erg.  This  is 
about  the  highest  value  of  energy  which  physicists 
have  yet  been  able  to  impart  to  an  electron. 

The  Inconstancy  of  Mass:  Mass  or  inertia,  as 
defined  on  page  40,  depends  upon  energy  and  speed. 
Neglect  for  the  moment  the  conventional  units  used 
in  this  Appendix  and  return  to  the  simple  units  of 
the  previous  text.  An  electron  moving  with  unit 
speed  (1  cm.  per  sec.)  has  unit  energy  and  under 
these  conditions  the  electron  has  unit  inertia.  If  it 
moves  with  twice  the  speed  it  has  four  times  the  en- 
ergy;  with  three  units  of  speed,  nine  units  of  energy; 
and  so  on,  the  energy  of  the  moving  electron  being 
equal  to  the  square  of  its  speed  as  long  as  this  speed 
is  small  as  compared  to  the  velocity  of  light  (3X1010 
cm.  per  second).  Under  these  conditions  the  inertia 
or  mass  of  the  electron  is  constant  and  is  measured 
by  the  ratio  of  the  number  of  units  of  energy  to  the 
square  of  the  number  of  units  of  speed. 

Actual  comparisons  have  been  made  of  the  ener- 
gies of  electrons  at  different  speeds  and  it  has  been 
found  that  as  higher  speeds  were  attained  the  energy 
was  increasing  enormously  faster  than  was  the 
square  of  the  velocity,  that  is,  that  the  inertia  of  an 
electron  is  not  constant  but  always  greater  for 
greater  speeds,  although  the  differences  are  imper- 
ceptible at  speeds  small  as  compared  to  light.  For 
this  reason  the  mass  may  be  said  to  be  inconstant. 
The  same  relation  holds  for  molar  bodies  as  well  as 


206  WITHIN  THE  ATOM 

electronic  if  we  accept,  as  we  must,  the  so-called 
"special  relativity  theory."  This  subject,  however, 
demands  a  whole  book  to  itself,  and  it  has  received 
many  such  in  recent  days. 


GLOSSARY 

ABSOLUTE  ZERO 

A  temperature  of  271.3°  below  zero  on  the  Centigrade 

scale,  equivalent  to  456.3°  below  zero  Fahrenheit. 
ABSORPTION  SPECTRUM 

A  spectrum  showing  by  their  absence  what  radiations 

a  given  substance  fails  to  transmit. 
ACIDS 

Electrolytes  for  which  one  product  of  dissociation  is 

a  hydrogen  ion. 
ALPHA  PARTICLES 

The  combination  of  four  protons  and  two  electrons 

which  is  expelled  from  the  nucleus  of  a  radioactive 

atom.    An  alpha  particle  is  identical  with  the  nucleus 

of  a  helium  atom. 
ALPHA  RAYS 

A  stream  of  alpha  particles. 
AMPERE 

A  unit  of  electrical  current.    See  Appendix. 
AMPHOTERIC 

A  term  applied  to  chemical  elements  which  react  either 

as  electropositive  or  electronegative  depending  on  the 

other  reactants. 
ANODE 

The  plate  or  other  terminal  in  a  conducting  gas  or 

liquid  at  which  electrons  or  negative  ions  are  collected. 

The  positive  electrode. 
ANTI-CATHODE 

The  anode  or  target  in  an  X-ray  tube. 
ATOM 

An  atomic  system  which  is  uncharged  having  equal 

numbers  of  protons  and  electrons. 
ATOMIC  NUMBER 

A  number  equal  to  the  number  of  positive  charges 

207 


208  WITHIN  THE  ATOM 

(protons)  of  a  nucleus  in  excess  of  the  number  of  nega- 
tive charges  (electrons). 

ATOMIC  SYSTEM 

A  nucleus  and  associated  planetary  electrons.  It  may 
be  either  a  normal  atom  or  an  ion. 

ATOMIC  WEIGHT 

The  number  representing,  on  a  scale  which  assigns  16 
to  oxygen,  the  average  mass  of  the  atom  of  any  chemi- 
cal substance. 

ATOM-MODEL 

A  theoretical  configuration  of  the  electrons  in  an  atom 
which  would  account  for  its  properties. 

BASES 

Electrolytes  for  which  one  dissociation  product  is  a 
negative  ion  formed  by  an  oxygen  and  a  hydrogen 
atom. 

BETA  PARTICLE 

An  electron  which  is  ejected  by  the  nucleus  of  a  radio- 
active atom. 

BETA  RAYS 
A  stream  of  beta  particles. 

CALORIE 
A  unit  of  energy  used  in  discussing  heat.    cf.  p.  178. 

CARBOHYDRATE 

A  chemical  compound  of  a  particular  type  which  con- 
tains carbon,  hydrogen  and  oxygen.  Of  this  type  the 
sugars  are  examples. 

CATHODE 

A  plate  or  other  terminal  in  a  conducting  gas  (or 
liquid)  at  which  positive  ions  are  collected  or  electrons 
are  emitted.  The  negative  electrode. 

CATHODE  RAYS 

A  stream  of  electrons  proceeding  outward  from  the 
cathode  of  a  tube  (of  gas)  which  is  conducting  elec- 
tricity. 

CENTIMETER 
Approximately  0.394  inch. 

CHARGE 

The  excess  of  positive  or  negative  electricity  in  a 
body. 


,      GLOSSARY  209 

CHEMICAL  ELEMENT 

A  substance  all  of  whose  atomic  systems  have  the  same 
atomic  number. 

CONTACT  ELECTROMOTIVE  FORCE 
The  potential  difference  which  is  set  up  by  the  contact 
of  two  dissimilar  substances,  i.  e.,  substances  with  dif- 
ferent electronic  structure. 

CONTINUOUS  SPECTRUM 
A  spectrum  which  includes  all  possible  frequencies. 

COULOMB 
A  unit  of  charge,    cf.  Appendix. 

DISSOCIATION 

A  disruption  of  a  molecular  system  which  may  or  not, 
as  the  case  may  be,  result  in  neutral  systems.  Elec- 
trolytes dissociate  into  charged  systems,  the  ions. 

DISINTEGRATION 
A  disruption  of  the  nucleus  of  an  atomic  system. 

DISINTEGRATION  PRODUCT 

The  atomic  system  which  results  when  alpha  or  beta 
particles  are  expelled  from  a  nucleus. 

ELECTRICAL  ELEMENTS 

The  electron  and  the  proton. 

ELECTRODE 

The  metal  plate  which  terminates  the  solid  portion 
of  an  electrically  conducting  path,  the  other  portion  of 
which  either  is  gaseous  or  liquid  or  is  a  vacuum. 

ELECTROLYTE 

A  solution  for  which  the  solute  partially  dissociates 
into  ions. 

ELECTROMAGNET 

A  piece  of  magnetic  material  about  which  is  wound 
a  current-carrying  loop  of  wire. 

ELECTROMAGNETIC  THEORY 

The  generally  accepted -theory  of  electricity  and  mag- 
netism which  was  formulated  by  Maxwell. 

ELECTROMETER 
An  instrument  for  measuring  an  electrical  charge. 

ELECTRON 

The  elementary  corpuscule  of  negative  electricity.  It 
is  complementary  to  the  proton. 


210  WITHIN  THE  ATOM 

ELECTRONEGATIVE 

A  term  applied  to  chemical  elements  whose  atoms  have 
a  negative  valence. 

ELECTROPOSITIVE 
The  opposite  of  electronegative. 

ELECTROSCOPE 
An  instrument  for  detecting  an  electrical  charge. 

ELECTROSTATIC 

A  term  applied  to  an  electrical  charge  which  is  fixed 
in  position. 

EMANATION 

The  name  applied  to  the  product  formed  by  the  ex- 
pulsion of  alpha  particles  from  the  nucleus  of  radium  or 
thorium  atoms.  In  this  book  radium  emanation  is 
called  "niton." 

EMISSION  SPECTRUM 

The  spectrum  of  the  radiation  from  a  body. 

ENERGY 

The  name  applied  to  the  motive  power  in  the  physical 

'    universe.     One  of  the   two   fundamental   entities  of 
modern  physics ;  the  other  is  electricity. 

ENTROPY 

A  numerical  expression  which  increases  as  energy  loses 
its  availability. 

ERG 
A  unit  of  energy,   cf.  Appendix. 

FLUORESCENT 

Giving  rise  to  radiations  of  other  frequencies  than 
those  which  it  absorbs. 

FREQUENCY 
Number  of  oscillations  per  second. 

GAMMA  RAYS 

A  radiation,  similar  in  type  to  X-rays,  which  proceeds 
outward  from  some  radioactive  atoms  when  the  sub- 
stance is  emitting  beta  rays. 

GRAM 
A  unit  of  mass  approximately  equal  to  0.0353  ounce. 

GRATING 

A  series  of  equally  spaced  reflecting  surfaces  which 
serve  to  analyse  radiations  into  their  component  fre- 
quencies. 


GLOSSARY  211 

INERTIA 

A  characteristic  unwillingness  to  change  in  state  of 
motion  which  all  bodies  display. 

INFRA-RED 

Of  lower  frequency  than  the  visible  radiation. 

INTERFEROMETER 

An  instrument  for  measuring  distances  very  accurately 
in  terms  of  wave  lengths  of  visible .  light.  Used  by 
Michelson  to  measure  the  international  meter. 

ION 

An  atomic  or  molecular  system  which  is  electrically 
charged  by  virtue  of  an  inequality  in  the  number  of 
its  protons  and  its  electrons. 

IONIZATION 

A  disruption  of  an  atom  or  molecule  into  ions  or  into 
ions  and  electrons. 

IONIZATION  POTENTIAL 

The  amount  of  potential  energy  which  must  be  con- 
verted into  kinetic  in  order  that  an  impact  of  the  body 
with  which  the  energy  is  associated  shall  ionize  an 
atom  or  molecule. 

ISOTOPE 

A  substance  which  occupies  with  another  substance 
the  same  place  in  the  periodic  table  of  chemical  ele- 
ments. The  two  substances  then  have  the  same  atomic 
number  but  different  atomic  masses. 

JOULE 
A  unit  of  energy,    cf.  Appendix. 

KINETIC  ENERGY 

Energy  associated  with  electricity  in  motion. 

LINE  SPECTRUM 

A  discontinuous  spectrum  formed  by  radiation  of  only 
certain  definite  frequencies. 

MASS 

The  amount  of  matter  in  a  body;  more  strictly,  a 
measure  of  its  ability  to  acquire  kinetic  energy. 

MOLE 

A  number  of  grams  of  a  given  substance  equal  to  the 
sum  of  the  atomic  weights  of  all  the  atoms  in  a  molecule 
of  the  substance. 


212  WITHIN  THE  ATOM 

MOLECULAR  HEAT 

The  heat  required  per  molecule  (strictly  per  mole)  to 
raise  the  temperature  of  a  substance  1°  centigrade. 

MOLECULAR  SYSTEM 

A  union  formed  by  two  or  more  atomic  systems.  It 
may  be  either  a  normal  molecule  or  an  ion. 

MOLECULE 

A  molecular  system  which  is  uncharged,  having  equal 
numbers  of  protons  and  electrons. 

NITON 
Radium  emanation.    An  inert  gas  of  atomic  number  86. 

NUCLEUS 

One  or  more  protons  associated  with  electrons  in  a  com- 
pact group  central  to  an  atomic  system. 

OSCILLATOR 

An  atomic  or  electronic  system  the  parts  of  which 
vibrate  or  oscillate. 

PELLATE 

Move  apart  except  as  restrained. 

PERIODIC  TABLE 

The  arrangement  of  the  chemical  elements,  in  ascend- 
ing order  of  atomic  numbers,  in  which  elements  of 
somewhat  similar  electronic  structure,  and  hence 
chemical  properties,  appear  periodically. 

PHOSPHORESCENT 

Emitting  radiation  as  a  result  of  radiation  which  is 
absorbed  but  after  absorption  has  ceased. 

PHOTO-ELECTRIC 

Pertaining  to  the  emission  of  electrons  which  occurs 
under  the  action  of  light. 

PLANCK'S  CONSTANT 

The  factor  of  proportionality  by  which  the  frequency 
of  an  electronic  oscillator  must  be  multiplied  in  order 
to  express  a  quantum  in  ergs. 

PLANETARY  ELECTRONS 

The  electrons  in  an  atom  which  are  external  to  the 
nucleus. 

POLYMERIZATION 

The  formation  of  aggregates  of  molecules  which  move 
about  (in  solution)  as  if  they  were  single  molecules. 


GLOSSARY  213 

POSITIVE  RAYS 

A  stream  of  positive  ions  from  a  tube  of  conducting 
gas. 

POTENTIAL  DIFFERENCE 

A  measure  of  the  potential  energy  which  is  available 
between  two  points. 

POTENTIAL  (ELECTRICAL) 

The  measure  of  the  potential  energy  which  is  associated 
with  a  unit  quantity  of  electricity. 

POTENTIAL  ENERGY 

Energy  which  it  is  assumed,  upon  the  basis  of  the 
conservation  of  energy,  is  associated  with  the  con- 
figuration of  electrical  systems. 

POTENTIAL  GRADIENT 

The  rate  at  which  the  potential  difference  between  two 
points  changes  as  the  position  of  one  is  varied. 

PROTON 

The  elementary  corpuscule  of  positive  electricity.  It 
is  complementary  to  the  electron. 

QUANTUM 

A  variable  amount  of  energy,  directly  proportional  to 
the  frequency  of  the  radiation  which  is  emitted  by  an 
electronic  oscillator. 

RADIATION 

Energy,  unassociated  with  matter,  which  is  being  trans- 
ferred through  space. 

RADIOACTIVE 

A  term  applied  to  substances  the  nuclei  of  whose  atoms 
spontaneously  disintegrate. 

RADIUM 

The  most  famous  radioactive  substance,  discovered 
by  the  Curies  in  1897. 

RE-RADIATION 

Radiation  emitted  by  a  body  which  is  absorbing  radia- 
tion from  a  distant  source. 

RESISTANCE  (ELECTRICAL) 

The  unwillingness  of  a  body  to  transmit  electricity, 
which  is  measured  by  the  ratio  of  an  electrical  potential 
(the  cause)  to  a  current  (the  effect) . 

RESONANCE  POTENTIAL 
The  amount  of  potential  energy  which  must  be  con- 


214  WITHIN  THE  ATOM 

verted  into  kinetic  in  order  that  an  impact  shall  excite 

the  characteristic  radiation  from  an  atom. 
SALTS 

Electrolytes  which  are  neither  acids  nor  bases. 
SCINTILLATION 

A  discrete  speck  of  light  produced  in  a  screen  by  the 

impact  of  a  high  speed  ion,  usually  of  an  alpha  particle. 
SOLENOID 

A  tubular  winding  of  wire  formed  by  spiralling  a  wire 

as  in  Fig.  4. 
SPECIFIC  HEAT 

Energy  required  to  raise  the  temperature  of  unit  mass 

of  a  substance  one  degree. 
SPECTROMETER 

An  instrument  for  the  quantitative  analysis  of  radia- 
tion into  its  component  frequencies. 
SPECTROSCOPE 

An  instrument  for  the  qualitative  investigation  of  the 

component  frequencies  of  a  given  radiation. 
SPECTRUM 

A  broad  band  of  radiation  in  which  the  several  com- 
ponent radiations  are  arranged  side  by  side  in  the 

order  of  their  frequencies. 
TEMPERATURE  ENCLOSURE 

A  region  surrounded  by  walls  which  are  maintained  at 

a  constant  temperature. 
TEMPERATURE  EQUILIBRIUM 

The  condition  of  a  system  the  parts  of  which  undergo 

no  relative  changes  in  temperature. 
TEMPERATURE  RADIATION 

Radiation  emitted  as  the  result  of  the  thermal  agitation 

in  a  body. 
THERMION 

An  electron  emitted  from  a  body  as  a  result  of  thermal 

agitation. 
THERMODYNAMIC  EFFICIENCY 

c/.  p.  186. 
THERMODYNAMIC  PROBABILITY 

c/.  p.  190. 
THERMODYNAMIC  SCALE  OF  TEMPERATURE 

A  temperature  scale  starting  from  the  absolute  zero. 


GLOSSARY  215 

THRESHOLD  FREQUENCY 

The  minimum  frequency  of  radiation  which  will  pro- 
duce photo-electric  effects. 

TRACTATE 

Move  toward  each  other  except  as  restrained. 

ULTRA-VIOLET 
Of  higher  frequency  than  visible  radiation. 

VALENCE 

A  numerical  statement  of  the  ability  of  atoms  to  com- 
bine, expressed  in  terms  of  the  combining  ability  of 
hydrogen  as  unity,  e.g.,  hydrogen,  sodium,  chlorine 
are  monovalent;  oxygen,  sulphur  and  zinc  are  divalent; 
phosphorus  and  boron  are  trivalent  and  carbon  and 
silicon  are  tetravalent. 

VELOCITY 

Rate  of  change  of  position,  that  is  speed,  measured  in 
distance  per  unit  of  time. 

VOLT 

A  unit  of  potential  difference,    cf.  Appendix. 

WATT 

A  unit  of  power,  that  is  of  the  rate  at  which  energy 
is  expended,  cf.  Appendix. 

WAVE  LENGTH 

The  distance  traversed  by  radiant  energy  in  the  period 
occupied  by  one  complete  oscillation  of  its  source. 
Numerically  equal  to  the  velocity  of  light  divided  by 
the  frequency. 

X-RAYS 

The  radiation  from  the  anode  or  target  of  a  vacuum 
tube,  when  the  anode  is  subjected  to  severe  bombard- 
ment by  a  cathode  stream. 


THE        NEWER        PHYSICS 

THE   ATOM 

By  A.  C.  CREHORE,  Ph.D. 

1920.         177  Pages.         5x7%.         Ills.         Postpaid,  $2.00 

THE  MYSTERY  OF  MATTER 
AND  ENERGY 

RECENT  PROGRESS  AS  TO  THE  STRUCTURE 
OF  MATTER 

By  A.  C.  CREHORE,  Ph.D. 

1917.     172  Pages.     4^x6^.     Cloth.     8  Plates  and  Folding 
Charts.     Postpaid,  $1.00 


THE  NATURE  OF  MATTER 
AND  ELECTRICITY 

4iV  OUTLINE  OF  MODERN  VIEWS 

By  DANIEL  F.  COMSTOCK,  S.B.,  Ph.D. 

Engineer  and  Associate  Professor  of  Theoretical  Physics  in 

the  Massachusetts  Institute  of  Technology 

and 

LEONARD  T.  TROLAND,  S.B.,  A.M.,  Ph.D. 

Instructor  in  Harvard  University 

1917.   225  Pages.    5^x8.   Cloth.   22  Illustrations.    11  Plates 
Postpaid,  $2.50 

D.   VAN    NOSTRAND    COMPANY 

Publishers  and  Booksellers 
8  WARREN   STREET  NEW  YORK 


LIGHT        AND        COLOR 


HTHREE  authoritative,  well  illustrated  books  writ- 
ten by  an  investigator  in  the  general  field  of 
color,  who  has  the  faculty  of  bringing  forth  scientific 
facts  in  such  a  manner  as  to  be  helpful  not  only  to 
scientists  but  to  those  interested  in  the  various  arts. 

By  M.  LUCKIESH 

Director  of  Applied  Science,  Nela  Research  Laboratories, 
National  Lamp  Works  of  General  Electric  Company 

COLOR 

AND   ITS  APPLICATIONS 

Second  Edition,  Revised  and  Enlarged 

431  Pages.  6x9.  Cloth.  Postpaid,  $4.50 

150  Illustrations.      4  Color  Plates.      21  Tables 


LIGHT  AND  SHADE 

AND   THEIR   APPLICATIONS 

277  Pages.  6x9.  Cloth.  Postpaid,  $3.00 

135  Illustrations.        10  Tables 


VISUAL  ILLUSIONS 

AND    THEIR    APPLICATIONS 

200  Pages.  6x9.  Cloth.  In  Press 

Fully  Illustrated 

D.   VAN    NOSTRAND    COMPANY 

Publishers  and  Booksellers 
8  WARREN  STREET  NEW  YORK 


Eminent  Chemists 
of  Our  Time 

By  BENJAMIN  HARROW,  Ph.D. 

Associate  in  Physiological  Chemistry,  Columbia  University 
Author  of  "From  Newton  to  Einstein" 


A  non-technical  account 
of  the  more  remarkable 
achievements  in  the  realm 
of  chemistry  as  exemplified 
by  the  life  and  work  of  the 
more  modern  chemists. 
There  is  hardly  a  chemist  of 
note  whose  work  is  not  men- 
tioned in  connection  with 
one  or  another  of  the  eleven 
following :  Perkin  and  Coal 
Tar  Dyes;  Mendeleeff  and 
the  Periodic  Law;  Richards 
and  Atomic  Weights;  Ram- 
say and  the  Gases  of  the 
Atmosphere ;  van't  Hoff  and 
Physical  Chemistry;  Arr- 
henius  and  the  Theory  of 
Electrolytic  Dissociation; 
Moissan  and  the  Electric 
Furnace;  Curie  and  Radi- 
um; Victor  Meyer  and  the 
Rise  of  Organic  Chemistry; 
Remsen  and  the  Rise  of 
Chemistry  in  America; 
Fischer  and  the  Chemistry 
of  Foods. 


The  book  has  all  the  interest  of  a 
work  of  fiction,  the  charm  of  a  spark- 
ling biography  and  the  romance  of 
expanding  life  overcoming  .obstacles 
and  making  conquests.  It  tells  the 
story  of  the  life,  work,  aspirations 
and  successes  of  eleven  men  who  have 
done  the  most  to  make  the  science  of 
chemistry  the  important  factor  that 
it  is  today  in  every  phase  of  our  lives. 
— Brooklyn  Daily  Eagle. 

Popular  charm  in  Professor  Har- 
row's work.  .  .  .  Decidedly  non- 
technical, yet  manages  to  convey  a 
wealth  of  information  ...  an  in- 
teresting and  informative  book. — 
N.  Y.  Tribune. 

Dr.  Harrow's  sketches  are  intelli- 
gently sympathetic,  critical  enough, 
and  interestingly  interpretative.  The 
book  will  appeal  to  the  general  reader 
as  well  as  to  the  special  student. — 
N.  Y.  Evening  Post. 

Chemical  literature  is  enriched  by 
such  contributions,  and  it  is  by  read- 
ing such  works  that  inspiration  for 
the  struggle  to  attain  is  brought  to 
the  younger  generation.  It  is  well  for 
the  chemist  to  know  his  family  tree. 
— The  Canadian  Chemical  Journal. 


250  Pages. 


5x7^. 


Illustrated.  Postpaid,  $2.50 


D.   VAN    NOSTRAND    COMPANY 

Publishers  and  Booksellers 
8   WARREN  STREET  NEW  YORK 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
This  book  is  DUE  on  the  last  date  stamped  below. 

Fine  schedule:  25  cents  on  first  day  overdue 

50  cents  on  fourth  day  overdue 
One  dollar  on  seventh  day  overdue. 


EN 


1  #47 
NOV  1  4  J947 


INEERING  LI 


RARY 


LD  21-100m-12,'46(A2012sl6)4120 


458439 

UNIVERSITY  OF  CALIFORNIA 
DEPARTMENT  OF  CIVH-  ENGINEER. 
KEUEY,  CALIFORNIA 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


